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Effect of particle polydispersity on particle concentration measurement by using laser Doppler anemometry
Experimental Thermal and Fluid Science 31 (2007) 839–847 www.elsevier.com/locate/etfs
Effect of particle polydispersity on particle concentration measurement by using laser Doppler anemometry Isßıl Ayrancı a
a,b
, Guillaume Pinguet c, Dany Escudie´ b,*, Nevin Selc¸uk a, Rodolphe Vaillon b, Fre´de´ric Andre´ b
Department of Chemical Engineering, Middle East Technical University, 06531 Ankara, Turkey b Centre de Thermique de Lyon (CETHIL CNRS-INSA Lyon-UCBL), 20 av. A. Einstein, 69621 Villeurbanne cedex, France c Laboratoire de Me´canique des Fluides et d’Acoustique, Ecole Centrale de Lyon, 36, av. Guy de Collongue, 69131 Ecully cedex, France Received 28 October 2005; received in revised form 22 March 2006; accepted 31 March 2006
Abstract Measurement of particle concentration by laser Doppler anemometry (LDA) is studied on a vertical air jet seeded by a powder disperser with controlled particle and air flow rates. Particle arrival rate is utilized to retrieve particle number densities from conventional LDA operation. The effect of polydisperse nature of the particles is assessed. Comparisons between measured and estimated particle number densities suggest that only a certain portion of the particle population with a particle size to fringe spacing ratio around unity can be detected. Results indicate that reliable measurement of absolute particle concentration is possible for a particle population of narrow size distribution with an average diameter equivalent to fringe spacing. Present number density measurement technique which is useful for practical purposes with conventional LDA systems is found to yield physically reasonable profiles in both laminar and turbulent regimes. 2006 Elsevier Inc. All rights reserved. Keywords: Particle number density; LDA; Particle-laden jet; Laminar; Turbulent
1. Introduction Laser Doppler anemometry (LDA) technique is one of the most widely used techniques for point velocity and turbulence measurements in gas or liquid flows. The velocity information is obtained from frequency of light scattered by particles, droplets or bubbles dispersed in the fluid. As this scattered light is a source of additional information on the particles, i.e., their size and concentration, extension of LDA to access such characteristics is a subject of significant interest in the field of multiphase flow diagnostics [1,2].
*
Corresponding author. Tel.: +33 4 72 43 88 10; fax: +33 4 72 43 88 11. E-mail address: [email protected] (D. Escudie´).
0894-1777/$ - see front matter 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2006.03.031
Two basic approaches for determination of particle concentration from LDA can be named as particle arrival rate approach and time ratio technique [1–3]. The first one makes use of the data rate of the signal processor as an indicator of the number of particles that pass the sample volume. The dispersed phase is assumed to be dilute enough so that the sample volume contains no more than one particle at a given time. Particle number density can be found by dividing the data rate by particle velocity and cross-section of detection volume perpendicular to the direction of particle path. Detection volume is defined as the volume from which scattering signals are received and it is not necessarily equivalent to the sample volume illuminated by the laser beams [4]. Important uncertainties in this approach arise from (i) determination of particle size dependent dimensions of the detection volume and (ii)
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Nomenclature Ac D0 df dp dp,j Dres Fj fv Ndata ne nm,av nm,i Qa
cross-section of probe volume (m2) pipe inside diameter (m) fringe spacing (m) particle diameter (m) diameter of particles in size class j (m) reservoir diameter (m) volume fraction of particles in size class j (dimensionless) particle volume fraction (ppm) number of bursts (number) estimated average number density (number/m3) measured average number density (number/m3) measured local number density at position i (number/m3) air flow rate (m3/s)
evaluation of detection volume cross-sectional area perpendicular to the particle trajectory. The particle arrival rate technique was presented in its simplest form by Durst et al., in panel 12.28 of [3], where the flow trajectory is assumed to be perpendicular to the fringe pattern of the probe volume and the detection volume is represented by the illuminated volume. Furthermore, the cross-sectional area was approximated by a rectangle circumferencing the elliptical cross-section of the illuminated volume. A derivative of the data rate approach based on normalized particle arrival frequencies was used for experimental analysis of turbulent particleladen gas flow in an in-line tube bank [5]. The global tendencies of the normalized profiles were found to be consistent with predictions. The other basic approach, time ratio technique, was again first described as a simple estimation method by [3] in panel 10.16. It is based on the ratio of the sum of the transit times of detected particles to the total time elapsed which yields fraction of time for which the particles are present in the sample volume provided that the range of the transit times is not too wide. Division of this fraction by sample volume gives local number density. Similar to the particle arrival rate approach, this method is also based on the assumption that the flow is dilute so that multiple particles cannot be in the sample volume at the same instant. As velocity is not directly involved, the uncertainties related to trajectory dependent cross-sectional area are eliminated in this technique. However particle size dependent dimensions of the detection volume is a potential source of error as in the previous approach. Moreover, in turbulent situations, a wide range of particle transit times may introduce further uncertainties. This technique was also presented by Sekoguchi et al. [6] for determination of volume fraction by using measured size information of each particle and the volume of the probe volume. It has
Qp r r0 Re Dt u u0 Vp Vp,av e k mp m h
volumetric flow rate of particles (m3/s) Radial position (m) pipe radius (m) Reynolds number (=u0 Æ D0/m) (dimensionless) record time (s) vertical velocity component (m/s) average velocity at pipe exit (m/s) volume of single particle (m3) size averaged single particle volume (m3) void fraction (dimensionless) wavelength (m) particle disperser piston speed (m/s) kinematic viscosity of air (m2/s) angle between intersecting beams ()
been incorporated in a commercial LDA/PDA system which was used to study cold flow behavior in a laboratory scale circulating fluidized bed combustor [7]. Comparisons between measured and predicted concentration profiles showed significant discrepancies despite the similarity in trends. This discrepancy was partially attributed to the fact that the flow was not dilute. The uncertainties associated with these two basic methods for particle concentration measurement were investigated and eliminated in recent studies. Yu and Rasmuson [8] presented mathematical description of the trajectory dependent cross-section of the ellipsoidal probe volume perpendicular to the direction of flow and applied the technique on a phase Doppler anemometry (PDA) system. PDA is a technique derived from LDA which evaluates phase information of the scattered light. The main output of the technique is local particle size distribution which favors determination of particle concentration as particle size dependence of detection volume can be accounted for [4,9]. Such an approach, introduced by Qiu and Sommerfeld [9], involves extension of the hardware and software of a PDA system for detection of the amplitude of the filtered Doppler signal in connection with the particle size. The approach was found to yield correct global mass flow rates and has found applications such as analysis of pneumatic transport [10]. Particle concentration profiles measured by this approach was found to be in agreement with laser-light sheet measurements [10]. More recently, Albrecht et al. [11] developed cross-sectional area difference method which takes variation of detection volume with particle size into consideration. The method can be applied to conventional LDA systems without hardware extension. In this approach, if the detectable threshold intensity is known, the dimensions of the ellipsoidal detection volume and cross-section of the detection volume can be calculated for each particle size. However, the method requires a cal-
I. Ayrancı et al. / Experimental Thermal and Fluid Science 31 (2007) 839–847
ibration procedure which makes use of particle samples of known size and known scattering behavior for experimental determination maximum intensity achieved for a particle of given diameter passing through the center of the measurement volume [4,11]. The method was reported to be particularly useful if it is combined with a PDA system which measures size distribution simultaneously [11]. Although it has been shown in previous studies that Doppler systems can be extended to particle concentration measurements by calibration procedures or additional detection systems, it is also important to investigate the possibility of determining absolute particle concentration from conventional LDA operation to be able to get maximum possible information out of already installed systems without any calibration. With this motivation, present contribution makes use of particle arrival rate approach which is a rather simple, straightforward but approximate methodology to extract particle concentration information from data rate on a vertical particle-laden air jet. Particle number densities measured by LDA with this approach are compared against average particle concentrations estimated by using the controlled operating parameters of the aerosol generation system. The effect of detectable particle size range on measurements is assessed.
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2. Experiments The experimental setup is presented in Fig. 1. A vertical air jet is seeded with particles and a LDA system at forward scattering mode is installed conventionally to make velocity measurements within the jet. 2.1. Aerosol generation Pressurized air from a utility compressor is supplied to a particle disperser (TSI Model 3410 Dry Powder Disperser). The operating principle of the seeder is based on rotary brush mechanism and is schematically displayed in Fig. 2. The volumetric flow rate of particles is dependent on powder cake compact density and piston speed, vp. The void fraction, e, of the cake which is assumed to be homogeneous, was measured each time the reservoir was loaded by recording powder weight and reservoir volume. The concentration of particles in the flow is dependent on compact density of the cake, the piston speed and air flow rate, the latter two being adjustable operating parameters. ZrO2 particles (Prolabo) with a reported mean diameter of 15.56 lm and a bulk density of 5.89 g/cm3 were used as seeding material. The particles were dried in an oven
Fig. 1. Experimental set-up.
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mounted vertically with a 30 cm straight region before the exit. 2.2. LDA system
Fig. 2. Aerosol generation with rotating brush mechanism.
beforehand to avoid agglomeration. Use was made of a particle size distribution (psd) data of the same product, previously measured by Malvern Mastersizer as a representative distribution. Psd by volume and corresponding number distributions are presented in Fig. 3. The aerosol produced by the seeder was carried to the measurement zone by a plastic tube of D0 = 6 mm internal diameter. The jet was produced at the exit of this tube that was
The two velocity component LDA system supplied by Dantec Dynamics consists of a two-color, three-beam optical arrangement utilizing the green and blue lines of argon– ion laser. The signals from the two sample volumes are detected by photomultiplier tubes and processed by two burst spectrum analyzers (Dantec BSA enhanced, 57N20/ 35). Relevant optical parameters are presented in Table 1. Radial velocity profiles of the axial velocity component were measured at 7 mm (1.2D0) downstream of the pipe exit with a 0.5 mm lateral increment. The air flow rate, Qa, and Reynolds number of the pipe flow at turbulent regime (Re P 4000) was determined by using the central velocity measurement which is well within the potential core for a turbulent jet and therefore is representative of the average velocity within the pipe. For laminar regime experiments (Re < 2100), the air flow rate entering the particle disperser was measured by a rotameter. LDA measurements were carried out at various flow and particle load conditions. Table 2 summarizes the operating conditions of the particle-laden air jet for laminar (runs 1–3) and turbulent regimes (runs 4–14). In the runs 1–7, air flow
25
volume %
20 15 10 5 0 0.05
0.23
0.53
1.23
2.83 dp (µm)
6.52
15.04
34.69
80.00
0.05
0.23
0.53
1.23
2.83 dp (µm)
6.52
15.04
34.69
80.00
1.E+03
number %
1.E+01 1.E-01 1.E-03 1.E-05 1.E-07
Fig. 3. Particle size distribution: (a) psd by volume; (b) psd by number.
I. Ayrancı et al. / Experimental Thermal and Fluid Science 31 (2007) 839–847 Table 1 Optical parameters of the LDA system BSA1
BSA2
Transmitting optics Laser wavelength (nm) Beam separation (mm) Beam Gaussian diameter Focal length (mm)
488 42.4986 1.35 600
514.5 42.4958 1.35 600
Probe volume Diameter of circular ellipsoid waist (mm) Length of ellipsoid axis (mm)
0.276 7.802
0.291 8.227
Receiving optics Scattering mode Focal length (mm) Off-axis angle Polar angle Coincidence window (ms)
Forward scattering 310 14.5 1 0.3
rate increases as the piston velocity, which controls the particle flow rate, is fixed. In the remaining runs particle load increases gradually, keeping the air flow rate constant as much as possible. 3. Analysis 3.1. Local and average particle concentration from LDA measurements Particle arrival rate approach is employed for determination of local particle concentration. The LDA system is configured to measure two velocity components from two sample volumes. As particles traverse this volume, scat-
843
tered signals from particles are detected and the time elapsed between the entry and exit of the particle are recorded. It is possible to calculate local particle density by using the number of bursts, Ndata, recorded at a certain period of time, Dt. These data relevant to particles detected by both detectors (coincident data) are collected from the data files. The local number density per unit volume at position i is evaluated from nm;i ¼
N data;i Dti ui Ac
ð1Þ
where ui represents the vertical velocity component measured by the LDA and Ac stands for the horizontal crosssection of the detection volume. As coincident data is used, the cross-section should be the cross-section of the intersection of the sample volumes of the two laser pairs. The illuminated volume of each laser pair is an ellipsoid with dimensions reported in Table 1. The cross-section of intersection of two ellipsoids is presented in Fig. 4. The angle between the axes of the ellipses was found as 4.2 from the beam separation and focal lengths given in Table 1. The cross-sectional area is approximated by a parallelogram. Its area, Ac, is graphically found to be 0.92 ± 0.05 mm2. Sample volume cross-section is an important parameter that affects measured number densities. Parallelogram approximation to the cross-section introduces ±5% error to the measured number densities but it is practical when compared with analytical computation of the intersection of two ellipses. On the other hand, approximating the cross-section with one of the ellipses, while using coincident data causes 50% underestimation in number densities and the coarser approximation of using
Table 2 Operating conditions of the experiments Run no.
Piston velocity vp (mm/h)
Particle flow rate Qp (m3/s)
Air flow rate Qa (m3/s)
Reynolds number Re (u0 Æ D0/m)
Particle volume fraction fv (Qp/Qa) (ppm)
1 2 3 4 5 6 7 8 9 10 11 12 13 14
60 60 60 60 60 60 60 30 40 50 70 82 100 150
1.01 · 109 1.01 · 109 1.01 · 109 1.45 · 109 1.47 · 109 1.47 · 109 1.47 · 109 7.55 · 1010 1.01 · 109 1.26 · 109 1.69 · 109 2.06 · 109 2.45 · 109 3.68 · 109
8.44 · 105 1.22 · 104 1.48 · 104 2.80 · 104 3.38 · 104 4.82 · 104 7.38 · 104 3.02 · 104 2.90 · 104 2.85 · 104 2.68 · 104 2.90 · 104 2.90 · 104 2.83 · 104
1187 1718 2077 3935 4756 6770 10,369 4241 4080 3999 3765 4082 4072 3974
12.0 8.3 6.8 5.2 4.3 3.0 2.0 2.5 3.5 4.4 6.3 7.1 8.4 13.0
Fig. 4. Horizontal cross-section of sample volume for coincident data in realistic aspect ratio.
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the circumferencing rectangle increases the error to 60%. Use of coincident data coming from two intersecting sample volumes in the present study instead of data from single sample volume is likely to reduce errors due to dependence of detection volume on particle size by partially excluding measurements from the outer region of the detection volume which are most sensitive regions to particle size. Once local particle densities are evaluated along the radius, an integrated average of measured number density, nm,av, is calculated for comparison with estimated particle concentration. 3.2. Estimation of particle concentration from seeder operation
where ne ¼
P
jF j
¼ 1. Eq. (4) then becomes
Qp Qa V p;av
ð6Þ
Main sources of error in determination of estimate number densities is the uncertainty in air flow rate measurement during laminar operation due to instabilities in the air flow rate and the uncertainty in void fraction due to possible inhomogeneities in powder cake. The first factor introduces ±9% uncertainty in laminar regime number densities and the second factor causes ±5% uncertainty in all estimated number densities. Number densities are plotted with error bars in the results section to indicate total combined errors. 3.3. Hypothetical cases for detectable particle size range
Average number of particles per unit volume is determined by using the seeding operating parameters for comparison with LDA measurements. Average number density across the jet cross-section is estimated from ne ¼
ð1 eÞ ðpD2res =4Þ vp 1 Qa Vp
ð2Þ
where Dres stands for the reservoir diameter, numerator of the first term is equal to Qp, the volumetric flow rate of particles dispersed in the flow by the seeder and Vp represents the volume of a single particle. The polydisperse nature of the particles can be taken into account by dividing the particle population with given psd into groups of particles of incremental size ranges. The number density for each particle group, j, of average effective diameter, dp,j, and volume fraction with respect to total particle volume, Fj, can be evaluated from ne;j ¼
Qp F j pd 3p;j =6
1 Qa
ð3Þ
Summing up over all size groups, the average estimated number density of a population of polydisperse particles within the jet becomes X Qp X Fj ne ¼ ð4Þ ne;j ¼ Q a pd 3p;j =6 j j One can define equivalent particle volume as follows: X 1 Fj ð5Þ ¼ V p;av pd 3p;j =6 j
Although it is not possible to determine local psd experimentally in the present study, in an attempt to evaluate the effect of particle polydispersity on number densities, several hypothetical situations were considered based on the particle size reported by the supplier and a representative psd presented in Fig. 3. Consideration of the polydisperse nature of particles has resulted in number densities which are 4 orders of magnitude greater than measured concentrations as shown in the next section. The fine tail of the psd which is invisible to the LDA system has a small volume fraction but comprises a very large number of particles as shown in the corresponding number distribution of the given psd (Fig. 3b). It is well known that very small particles can not be detected by the LDA system because they have weak scattering signals. On the other hand, particles with size much greater than fringe spacing result in low visibility and hence, signal quality [3, panel 4.18]. In [3, panel 6.4], it is mentioned that the particle diameter to fringe spacing ratio of the order of 0.5–2.0 provided good signal to noise ratio in a previous study. Based on this finding, hypothetical cases were set up to determine the size range that can be detected. The fringe spacing can be found from df ¼
k 2 sinðh=2Þ
ð7Þ
where h represents the angle between the two intersecting beams of wavelength k and can be found from the optical parameters given in Table 1. Fringe spacing for 488 nm and 514.5 nm wavelengths were found to be 6.894 lm and 7.268 lm, respectively. An average value of 7 lm is taken
Table 3 Properties of the particle populations under consideration Case
Description
dp,av (lm)
Fi
Vp,av (lm3)
dp/df
MD PD1 PD2 PD3 PD4
Uniform particle size with reported mean diameter Polydisperse full size range (Fig. 3) 3.49 6 dp < 15.04 lm 5.29 6 dp < 9.91 lm 6.52 6 dp < 8.04 lm
15.56 1.15 8.72 7.56 7.28
1.0 1.0 0.4912 0.1313 0.0385
1973 0.8 346.7 226.0 202.0
0.5–2.14 0.76–1.42 0.93–1.15
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as the fringe spacing for the system under consideration. The particle size range corresponding to the reported dp/df range of 0.5–2.0 is 3.5–14 lm. Several detectable particle size ranges were assumed based on the particle size distribution in Fig. 3. These hypothetical cases are summarized in Table 3. The cases for uniform particle size with reported mean diameter and full range polydisperse size distribution are denoted by MD and PD1, respectively. PD2 was taken according to the criterion mentioned above but the estimated number density with this assumption was greater than the measured number density. Therefore two other cases were generated by narrowing the detectable size window around dp/df = 1. The comparisons between estimated number densities for these cases and measurements are presented in the next section. 4. Results and discussion Radial profiles of vertical velocity component measured by LDA for the runs summarized in Table 2 are presented in Fig. 5. In accordance with expected trends, when particle flow rate is kept constant and air flow rate is increased, the velocity profiles also increase (Fig. 5a) and the velocity pro-
Fig. 6. Number density profiles measured by LDA: (a) effect of air flow rate on number density; (b) effect of particle flow rate on number density.
Fig. 5. Velocity profiles: (a) effect of air flow rate on velocity; (b) effect of particle flow rate on velocity.
file does not change significantly when only particle flow rate is changed (Fig. 5b). In the latter case, the variations of ±0.5 m/s among the profiles are due to instabilities in the utility air pressure. Number densities obtained from LDA measurements by using Eq. (1) are presented in Fig. 6. Fig. 6a displays evolution of number density profile in the jet with increasing air flow rate when level of particle flow rate is kept constant. At runs 1–3 corresponding to laminar regime, the particles are concentrated within an annular region at around r/r0 = 0.5–0.7 mm. After the transition to turbulent regime the number densities homogenize. As the air flow rate is further increased, the concentrations decrease due to dilution by air and at the axial position under consideration, the jet enlarges due to the influence of turbulence on jet development. The variation of particle number density profiles with increasing particle load at Reynolds number around 4000 is presented in Fig. 6b. It is observed that as the particle load is increased above a certain threshold, the particles are drifted outwards resulting in a high density annular region. This non-homogeneous density profile is maintained in the turbulent high particle load cases but the radius and width of this concentrated ring is larger when compared to laminar case because of larger jet diameter. The ratio of ring thickness to jet radius is observed to
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I. Ayrancı et al. / Experimental Thermal and Fluid Science 31 (2007) 839–847
be nearly the same in both regimes, i.e., 0.6 in laminar case, 0.55 in turbulent case. There are various possible causes for concentrated annular regions which are observed for particle loads higher than fv = 6 ppm in both laminar and turbulent cases. The two-phase flow within the pipe can be considered as vertical, fully developed, dilute phase, pneumatic conveying regime. The governing equations for this kind of flow indicate that the radial particle concentration distribution is dependent on electrostatic interactions and particles tend to concentrate near the pipe walls if the electrostatic charge carried by each particle is significant [12]. As the pipe material is plastic and the particles are ZrO2 which has a high dielectric constant, effects of electrostatic charging are expected to prevail within the pipe so that the particle density distribution is non-homogeneous at the pipe exit. Within the jet, particle dispersion takes place depending upon the Reynolds number and particle concentration. The reason for the concentrated ring structure measurements at high particle load conditions is that, dispersion of particles up to the measurement location at 1.2D axial position is not adequate to homogenize the initial heterogeneous distribution at the pipe exit. Another factor can be due to the dynamics within the jet, i.e., at high
particle concentrations the particles can be drifted towards the jet boundaries due to lower velocities in this region. Such concentrated annular regions in particle-laden free jets were also observed by Pothos and Longmire [13]. Measured profiles indicate that present methodology used to extract particle concentration information from LDA data provides physically reasonable local number density measurements. In an attempt to assess the reliability of the number density measurements, cross-sectional average of measured profiles are compared with estimated number densities based on the hypothetical cases of different detectable particle size ranges, as defined in Section 3.3. Fig. 7a shows the variation with Reynolds number for constant particle load and variable air flow rate and Fig. 7b displays variation of number densities with particle load for constant Re around 4000. As can be seen from the figures, measurements and estimates follow similar trends of variation but the absolute values of estimates are strongly dependent on the polydisperse nature of particles and detectable particle size range. The slightly steeper slope in Fig. 6a for the estimates of laminar runs when compared with the slope in turbulent cases is due to slightly different particle flow rates caused by void fraction difference in the seeder powder reservoir for laminar and turbulent regimes. The assumption of monodisperse particles (MD) results in significant difference between measurements and estimates. Consideration of the complete particle size distribution (PD1) results about 4 orders of magnitude more particles than measurements. This is due to the fine tail of the psd which is counted in the estimate but actually can not be detected in the measurement. In order to get an indication on the size of the particles visible to the LDA system, the size distribution range was narrowed gradually around dp/df = 1 as explained in Section 3.3. PD2 results are about an order of magnitude greater than the measurements. As the detectable particle diameter range gets narrower towards PD3 case, the number density estimates decrease and PD4 case produces estimates in favorable agreement with measurements. This outcome suggests that the detectable particle size window for the LDA system and the seeding material under consideration is 0.93 < dp/df < 1.15. 5. Practical significance
Fig. 7. Variation of measured and estimated number densities with flow conditions: (a) effect of Reynolds number; (b) effect of particle flow rate.
The methodology investigated in this study can be used to access local particle number density information in multiple phase flows from conventional LDA measurements without calibration or hardware extension. The method is found to be useful as a simple approach for relative concentration measurements. The results suggest that the size range of particles that can be counted by LDA is limited around particle size to fringe spacing ratio of unity and therefore reliable absolute concentration measurements are possible if the particles have narrow size distribution within this range.
I. Ayrancı et al. / Experimental Thermal and Fluid Science 31 (2007) 839–847
6. Conclusion A practical methodology for measurement of local particle number densities by using laser Doppler anemometry was studied on a vertical air jet seeded with controlled particle and air flow rates. Similar trends with estimates indicate that the present approach is applicable for measurement of local particle concentration and it can be used for relative measurements. The absolute LDA measurements are highly sensitive to the detectable particle size range and the size distribution of the sample particles. In order to make reliable absolute particle concentration measurements with LDA, it is important to apply this technique to particle populations with narrow size distribution around a particle diameter equal to the fringe spacing. Otherwise, a certain portion of the particles may become invisible to the detector. Present methodology is a simple and practical option for determination of particle concentration in particle-laden flows but necessitates prudent interpretation in terms of detectable particle size range. The number densities measured by this method represent local concentrations of particles of about the same size as fringe spacing. Acknowledgements Isßıl Ayrancı was supported by a French government scholarship granted by the Embassy of France in Turkey within the frame of a joint PhD program co-supervised by METU and INSA de Lyon. This study was partially supported by the French Ministry of Research (Re´seau de Recherche et d’Innovation Technologique: ‘‘Recherche Ae´ronautique sur le Supersonique’’, de´cision no. 03T233). References [1] J. Chaouki, F. Larachi, M.P. Dudukovic, Noninvasive tomographic and velocimetric monitoring of multiphase flows, Industrial & Engineering Chemistry Research 36 (11) (1997) 4476–4503.
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[2] S. Shao, Study of the flow behavior of multiphase system using laser Doppler anemometry (LDA), PhD Thesis, Illinois Institute of Technology, 1996. [3] F. Durst, A. Melling, J.H. Whitelaw, Principles and Practice of Laser Doppler Anemometry, Academic Press, London, 1981. [4] H.-E. Albrecht, M. Borys, N. Damaschke, C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques, Springer, Germany, 2003. [5] J.Y. Tu, C.A.J. Fletcher, Y.S. Morsi, W. Yang, M. Behnia, Numerical and experimental studies of turbulent particle-laden gas flow in an in-line tube bank, Chemical Engineering Science 53 (2) (1998) 225–238. [6] K. Sekoguchi, M. Takeishi, H. Kano, K. Hironaga, T. Nishiura, The measurement and calculation of furnace flow properties, in: 1st International Symposium on Application of Laser Anemometry to Fluid Mechanics, Lisbon, Portugal, 1982, Paper 16.1. [7] V. Mathiesen, T. Solberg, B.H. Hjertager, An experimental and computational study of multiphase flow behavior in a circulating fluidized bed, International Journal of Multiphase Flow 26 (3) (2000) 387–419. [8] Z. Yu, A.C. Rasmuson, Projected area of measurement volume in phase-Doppler anemometry and application for velocity bias correction and particle concentration estimation, Experiments in Fluids 27 (2) (1999) 189–198. [9] H.H. Qiu, M. Sommerfeld, A reliable method for determining the measurement volume size and particle mass fluxes using phaseDoppler anemometry, Experiments in Fluids 13 (6) (1992) 393– 404. [10] N. Huber, M. Sommerfeld, Characterization of the cross-sectional particle concentration distribution in pneumatic conveying systems, Powder Technology 79 (3) (1994) 191–210. [11] H.E. Albrecht, M. Borys, W. Fuchs, The cross-sectional area difference method – a new technique for determination of particle concentration by laser-Doppler anemometry, Experiments in Fluids 16 (1) (1993) 61–69. [12] L.-S. Fan, C. Zhu, Principles of gas–solid flows, in: A. Varma (Ed.), Cambridge Series in Chemical Engineering, Cambridge University Press, UK, 1998, p. 482. [13] S. Pothos, E.K. Longmire, Control of a particle-laden jet using a piezo-electric actuator, in: 11th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 2002.
Effect of particle polydispersity on particle concentration measurement by using laser Doppler anemometry Isßıl Ayrancı a
a,b
, Guillaume Pinguet c, Dany Escudie´ b,*, Nevin Selc¸uk a, Rodolphe Vaillon b, Fre´de´ric Andre´ b
Department of Chemical Engineering, Middle East Technical University, 06531 Ankara, Turkey b Centre de Thermique de Lyon (CETHIL CNRS-INSA Lyon-UCBL), 20 av. A. Einstein, 69621 Villeurbanne cedex, France c Laboratoire de Me´canique des Fluides et d’Acoustique, Ecole Centrale de Lyon, 36, av. Guy de Collongue, 69131 Ecully cedex, France Received 28 October 2005; received in revised form 22 March 2006; accepted 31 March 2006
Abstract Measurement of particle concentration by laser Doppler anemometry (LDA) is studied on a vertical air jet seeded by a powder disperser with controlled particle and air flow rates. Particle arrival rate is utilized to retrieve particle number densities from conventional LDA operation. The effect of polydisperse nature of the particles is assessed. Comparisons between measured and estimated particle number densities suggest that only a certain portion of the particle population with a particle size to fringe spacing ratio around unity can be detected. Results indicate that reliable measurement of absolute particle concentration is possible for a particle population of narrow size distribution with an average diameter equivalent to fringe spacing. Present number density measurement technique which is useful for practical purposes with conventional LDA systems is found to yield physically reasonable profiles in both laminar and turbulent regimes. 2006 Elsevier Inc. All rights reserved. Keywords: Particle number density; LDA; Particle-laden jet; Laminar; Turbulent
1. Introduction Laser Doppler anemometry (LDA) technique is one of the most widely used techniques for point velocity and turbulence measurements in gas or liquid flows. The velocity information is obtained from frequency of light scattered by particles, droplets or bubbles dispersed in the fluid. As this scattered light is a source of additional information on the particles, i.e., their size and concentration, extension of LDA to access such characteristics is a subject of significant interest in the field of multiphase flow diagnostics [1,2].
*
Corresponding author. Tel.: +33 4 72 43 88 10; fax: +33 4 72 43 88 11. E-mail address: [email protected] (D. Escudie´).
0894-1777/$ - see front matter 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2006.03.031
Two basic approaches for determination of particle concentration from LDA can be named as particle arrival rate approach and time ratio technique [1–3]. The first one makes use of the data rate of the signal processor as an indicator of the number of particles that pass the sample volume. The dispersed phase is assumed to be dilute enough so that the sample volume contains no more than one particle at a given time. Particle number density can be found by dividing the data rate by particle velocity and cross-section of detection volume perpendicular to the direction of particle path. Detection volume is defined as the volume from which scattering signals are received and it is not necessarily equivalent to the sample volume illuminated by the laser beams [4]. Important uncertainties in this approach arise from (i) determination of particle size dependent dimensions of the detection volume and (ii)
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Nomenclature Ac D0 df dp dp,j Dres Fj fv Ndata ne nm,av nm,i Qa
cross-section of probe volume (m2) pipe inside diameter (m) fringe spacing (m) particle diameter (m) diameter of particles in size class j (m) reservoir diameter (m) volume fraction of particles in size class j (dimensionless) particle volume fraction (ppm) number of bursts (number) estimated average number density (number/m3) measured average number density (number/m3) measured local number density at position i (number/m3) air flow rate (m3/s)
evaluation of detection volume cross-sectional area perpendicular to the particle trajectory. The particle arrival rate technique was presented in its simplest form by Durst et al., in panel 12.28 of [3], where the flow trajectory is assumed to be perpendicular to the fringe pattern of the probe volume and the detection volume is represented by the illuminated volume. Furthermore, the cross-sectional area was approximated by a rectangle circumferencing the elliptical cross-section of the illuminated volume. A derivative of the data rate approach based on normalized particle arrival frequencies was used for experimental analysis of turbulent particleladen gas flow in an in-line tube bank [5]. The global tendencies of the normalized profiles were found to be consistent with predictions. The other basic approach, time ratio technique, was again first described as a simple estimation method by [3] in panel 10.16. It is based on the ratio of the sum of the transit times of detected particles to the total time elapsed which yields fraction of time for which the particles are present in the sample volume provided that the range of the transit times is not too wide. Division of this fraction by sample volume gives local number density. Similar to the particle arrival rate approach, this method is also based on the assumption that the flow is dilute so that multiple particles cannot be in the sample volume at the same instant. As velocity is not directly involved, the uncertainties related to trajectory dependent cross-sectional area are eliminated in this technique. However particle size dependent dimensions of the detection volume is a potential source of error as in the previous approach. Moreover, in turbulent situations, a wide range of particle transit times may introduce further uncertainties. This technique was also presented by Sekoguchi et al. [6] for determination of volume fraction by using measured size information of each particle and the volume of the probe volume. It has
Qp r r0 Re Dt u u0 Vp Vp,av e k mp m h
volumetric flow rate of particles (m3/s) Radial position (m) pipe radius (m) Reynolds number (=u0 Æ D0/m) (dimensionless) record time (s) vertical velocity component (m/s) average velocity at pipe exit (m/s) volume of single particle (m3) size averaged single particle volume (m3) void fraction (dimensionless) wavelength (m) particle disperser piston speed (m/s) kinematic viscosity of air (m2/s) angle between intersecting beams ()
been incorporated in a commercial LDA/PDA system which was used to study cold flow behavior in a laboratory scale circulating fluidized bed combustor [7]. Comparisons between measured and predicted concentration profiles showed significant discrepancies despite the similarity in trends. This discrepancy was partially attributed to the fact that the flow was not dilute. The uncertainties associated with these two basic methods for particle concentration measurement were investigated and eliminated in recent studies. Yu and Rasmuson [8] presented mathematical description of the trajectory dependent cross-section of the ellipsoidal probe volume perpendicular to the direction of flow and applied the technique on a phase Doppler anemometry (PDA) system. PDA is a technique derived from LDA which evaluates phase information of the scattered light. The main output of the technique is local particle size distribution which favors determination of particle concentration as particle size dependence of detection volume can be accounted for [4,9]. Such an approach, introduced by Qiu and Sommerfeld [9], involves extension of the hardware and software of a PDA system for detection of the amplitude of the filtered Doppler signal in connection with the particle size. The approach was found to yield correct global mass flow rates and has found applications such as analysis of pneumatic transport [10]. Particle concentration profiles measured by this approach was found to be in agreement with laser-light sheet measurements [10]. More recently, Albrecht et al. [11] developed cross-sectional area difference method which takes variation of detection volume with particle size into consideration. The method can be applied to conventional LDA systems without hardware extension. In this approach, if the detectable threshold intensity is known, the dimensions of the ellipsoidal detection volume and cross-section of the detection volume can be calculated for each particle size. However, the method requires a cal-
I. Ayrancı et al. / Experimental Thermal and Fluid Science 31 (2007) 839–847
ibration procedure which makes use of particle samples of known size and known scattering behavior for experimental determination maximum intensity achieved for a particle of given diameter passing through the center of the measurement volume [4,11]. The method was reported to be particularly useful if it is combined with a PDA system which measures size distribution simultaneously [11]. Although it has been shown in previous studies that Doppler systems can be extended to particle concentration measurements by calibration procedures or additional detection systems, it is also important to investigate the possibility of determining absolute particle concentration from conventional LDA operation to be able to get maximum possible information out of already installed systems without any calibration. With this motivation, present contribution makes use of particle arrival rate approach which is a rather simple, straightforward but approximate methodology to extract particle concentration information from data rate on a vertical particle-laden air jet. Particle number densities measured by LDA with this approach are compared against average particle concentrations estimated by using the controlled operating parameters of the aerosol generation system. The effect of detectable particle size range on measurements is assessed.
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2. Experiments The experimental setup is presented in Fig. 1. A vertical air jet is seeded with particles and a LDA system at forward scattering mode is installed conventionally to make velocity measurements within the jet. 2.1. Aerosol generation Pressurized air from a utility compressor is supplied to a particle disperser (TSI Model 3410 Dry Powder Disperser). The operating principle of the seeder is based on rotary brush mechanism and is schematically displayed in Fig. 2. The volumetric flow rate of particles is dependent on powder cake compact density and piston speed, vp. The void fraction, e, of the cake which is assumed to be homogeneous, was measured each time the reservoir was loaded by recording powder weight and reservoir volume. The concentration of particles in the flow is dependent on compact density of the cake, the piston speed and air flow rate, the latter two being adjustable operating parameters. ZrO2 particles (Prolabo) with a reported mean diameter of 15.56 lm and a bulk density of 5.89 g/cm3 were used as seeding material. The particles were dried in an oven
Fig. 1. Experimental set-up.
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mounted vertically with a 30 cm straight region before the exit. 2.2. LDA system
Fig. 2. Aerosol generation with rotating brush mechanism.
beforehand to avoid agglomeration. Use was made of a particle size distribution (psd) data of the same product, previously measured by Malvern Mastersizer as a representative distribution. Psd by volume and corresponding number distributions are presented in Fig. 3. The aerosol produced by the seeder was carried to the measurement zone by a plastic tube of D0 = 6 mm internal diameter. The jet was produced at the exit of this tube that was
The two velocity component LDA system supplied by Dantec Dynamics consists of a two-color, three-beam optical arrangement utilizing the green and blue lines of argon– ion laser. The signals from the two sample volumes are detected by photomultiplier tubes and processed by two burst spectrum analyzers (Dantec BSA enhanced, 57N20/ 35). Relevant optical parameters are presented in Table 1. Radial velocity profiles of the axial velocity component were measured at 7 mm (1.2D0) downstream of the pipe exit with a 0.5 mm lateral increment. The air flow rate, Qa, and Reynolds number of the pipe flow at turbulent regime (Re P 4000) was determined by using the central velocity measurement which is well within the potential core for a turbulent jet and therefore is representative of the average velocity within the pipe. For laminar regime experiments (Re < 2100), the air flow rate entering the particle disperser was measured by a rotameter. LDA measurements were carried out at various flow and particle load conditions. Table 2 summarizes the operating conditions of the particle-laden air jet for laminar (runs 1–3) and turbulent regimes (runs 4–14). In the runs 1–7, air flow
25
volume %
20 15 10 5 0 0.05
0.23
0.53
1.23
2.83 dp (µm)
6.52
15.04
34.69
80.00
0.05
0.23
0.53
1.23
2.83 dp (µm)
6.52
15.04
34.69
80.00
1.E+03
number %
1.E+01 1.E-01 1.E-03 1.E-05 1.E-07
Fig. 3. Particle size distribution: (a) psd by volume; (b) psd by number.
I. Ayrancı et al. / Experimental Thermal and Fluid Science 31 (2007) 839–847 Table 1 Optical parameters of the LDA system BSA1
BSA2
Transmitting optics Laser wavelength (nm) Beam separation (mm) Beam Gaussian diameter Focal length (mm)
488 42.4986 1.35 600
514.5 42.4958 1.35 600
Probe volume Diameter of circular ellipsoid waist (mm) Length of ellipsoid axis (mm)
0.276 7.802
0.291 8.227
Receiving optics Scattering mode Focal length (mm) Off-axis angle Polar angle Coincidence window (ms)
Forward scattering 310 14.5 1 0.3
rate increases as the piston velocity, which controls the particle flow rate, is fixed. In the remaining runs particle load increases gradually, keeping the air flow rate constant as much as possible. 3. Analysis 3.1. Local and average particle concentration from LDA measurements Particle arrival rate approach is employed for determination of local particle concentration. The LDA system is configured to measure two velocity components from two sample volumes. As particles traverse this volume, scat-
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tered signals from particles are detected and the time elapsed between the entry and exit of the particle are recorded. It is possible to calculate local particle density by using the number of bursts, Ndata, recorded at a certain period of time, Dt. These data relevant to particles detected by both detectors (coincident data) are collected from the data files. The local number density per unit volume at position i is evaluated from nm;i ¼
N data;i Dti ui Ac
ð1Þ
where ui represents the vertical velocity component measured by the LDA and Ac stands for the horizontal crosssection of the detection volume. As coincident data is used, the cross-section should be the cross-section of the intersection of the sample volumes of the two laser pairs. The illuminated volume of each laser pair is an ellipsoid with dimensions reported in Table 1. The cross-section of intersection of two ellipsoids is presented in Fig. 4. The angle between the axes of the ellipses was found as 4.2 from the beam separation and focal lengths given in Table 1. The cross-sectional area is approximated by a parallelogram. Its area, Ac, is graphically found to be 0.92 ± 0.05 mm2. Sample volume cross-section is an important parameter that affects measured number densities. Parallelogram approximation to the cross-section introduces ±5% error to the measured number densities but it is practical when compared with analytical computation of the intersection of two ellipses. On the other hand, approximating the cross-section with one of the ellipses, while using coincident data causes 50% underestimation in number densities and the coarser approximation of using
Table 2 Operating conditions of the experiments Run no.
Piston velocity vp (mm/h)
Particle flow rate Qp (m3/s)
Air flow rate Qa (m3/s)
Reynolds number Re (u0 Æ D0/m)
Particle volume fraction fv (Qp/Qa) (ppm)
1 2 3 4 5 6 7 8 9 10 11 12 13 14
60 60 60 60 60 60 60 30 40 50 70 82 100 150
1.01 · 109 1.01 · 109 1.01 · 109 1.45 · 109 1.47 · 109 1.47 · 109 1.47 · 109 7.55 · 1010 1.01 · 109 1.26 · 109 1.69 · 109 2.06 · 109 2.45 · 109 3.68 · 109
8.44 · 105 1.22 · 104 1.48 · 104 2.80 · 104 3.38 · 104 4.82 · 104 7.38 · 104 3.02 · 104 2.90 · 104 2.85 · 104 2.68 · 104 2.90 · 104 2.90 · 104 2.83 · 104
1187 1718 2077 3935 4756 6770 10,369 4241 4080 3999 3765 4082 4072 3974
12.0 8.3 6.8 5.2 4.3 3.0 2.0 2.5 3.5 4.4 6.3 7.1 8.4 13.0
Fig. 4. Horizontal cross-section of sample volume for coincident data in realistic aspect ratio.
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the circumferencing rectangle increases the error to 60%. Use of coincident data coming from two intersecting sample volumes in the present study instead of data from single sample volume is likely to reduce errors due to dependence of detection volume on particle size by partially excluding measurements from the outer region of the detection volume which are most sensitive regions to particle size. Once local particle densities are evaluated along the radius, an integrated average of measured number density, nm,av, is calculated for comparison with estimated particle concentration. 3.2. Estimation of particle concentration from seeder operation
where ne ¼
P
jF j
¼ 1. Eq. (4) then becomes
Qp Qa V p;av
ð6Þ
Main sources of error in determination of estimate number densities is the uncertainty in air flow rate measurement during laminar operation due to instabilities in the air flow rate and the uncertainty in void fraction due to possible inhomogeneities in powder cake. The first factor introduces ±9% uncertainty in laminar regime number densities and the second factor causes ±5% uncertainty in all estimated number densities. Number densities are plotted with error bars in the results section to indicate total combined errors. 3.3. Hypothetical cases for detectable particle size range
Average number of particles per unit volume is determined by using the seeding operating parameters for comparison with LDA measurements. Average number density across the jet cross-section is estimated from ne ¼
ð1 eÞ ðpD2res =4Þ vp 1 Qa Vp
ð2Þ
where Dres stands for the reservoir diameter, numerator of the first term is equal to Qp, the volumetric flow rate of particles dispersed in the flow by the seeder and Vp represents the volume of a single particle. The polydisperse nature of the particles can be taken into account by dividing the particle population with given psd into groups of particles of incremental size ranges. The number density for each particle group, j, of average effective diameter, dp,j, and volume fraction with respect to total particle volume, Fj, can be evaluated from ne;j ¼
Qp F j pd 3p;j =6
1 Qa
ð3Þ
Summing up over all size groups, the average estimated number density of a population of polydisperse particles within the jet becomes X Qp X Fj ne ¼ ð4Þ ne;j ¼ Q a pd 3p;j =6 j j One can define equivalent particle volume as follows: X 1 Fj ð5Þ ¼ V p;av pd 3p;j =6 j
Although it is not possible to determine local psd experimentally in the present study, in an attempt to evaluate the effect of particle polydispersity on number densities, several hypothetical situations were considered based on the particle size reported by the supplier and a representative psd presented in Fig. 3. Consideration of the polydisperse nature of particles has resulted in number densities which are 4 orders of magnitude greater than measured concentrations as shown in the next section. The fine tail of the psd which is invisible to the LDA system has a small volume fraction but comprises a very large number of particles as shown in the corresponding number distribution of the given psd (Fig. 3b). It is well known that very small particles can not be detected by the LDA system because they have weak scattering signals. On the other hand, particles with size much greater than fringe spacing result in low visibility and hence, signal quality [3, panel 4.18]. In [3, panel 6.4], it is mentioned that the particle diameter to fringe spacing ratio of the order of 0.5–2.0 provided good signal to noise ratio in a previous study. Based on this finding, hypothetical cases were set up to determine the size range that can be detected. The fringe spacing can be found from df ¼
k 2 sinðh=2Þ
ð7Þ
where h represents the angle between the two intersecting beams of wavelength k and can be found from the optical parameters given in Table 1. Fringe spacing for 488 nm and 514.5 nm wavelengths were found to be 6.894 lm and 7.268 lm, respectively. An average value of 7 lm is taken
Table 3 Properties of the particle populations under consideration Case
Description
dp,av (lm)
Fi
Vp,av (lm3)
dp/df
MD PD1 PD2 PD3 PD4
Uniform particle size with reported mean diameter Polydisperse full size range (Fig. 3) 3.49 6 dp < 15.04 lm 5.29 6 dp < 9.91 lm 6.52 6 dp < 8.04 lm
15.56 1.15 8.72 7.56 7.28
1.0 1.0 0.4912 0.1313 0.0385
1973 0.8 346.7 226.0 202.0
0.5–2.14 0.76–1.42 0.93–1.15
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as the fringe spacing for the system under consideration. The particle size range corresponding to the reported dp/df range of 0.5–2.0 is 3.5–14 lm. Several detectable particle size ranges were assumed based on the particle size distribution in Fig. 3. These hypothetical cases are summarized in Table 3. The cases for uniform particle size with reported mean diameter and full range polydisperse size distribution are denoted by MD and PD1, respectively. PD2 was taken according to the criterion mentioned above but the estimated number density with this assumption was greater than the measured number density. Therefore two other cases were generated by narrowing the detectable size window around dp/df = 1. The comparisons between estimated number densities for these cases and measurements are presented in the next section. 4. Results and discussion Radial profiles of vertical velocity component measured by LDA for the runs summarized in Table 2 are presented in Fig. 5. In accordance with expected trends, when particle flow rate is kept constant and air flow rate is increased, the velocity profiles also increase (Fig. 5a) and the velocity pro-
Fig. 6. Number density profiles measured by LDA: (a) effect of air flow rate on number density; (b) effect of particle flow rate on number density.
Fig. 5. Velocity profiles: (a) effect of air flow rate on velocity; (b) effect of particle flow rate on velocity.
file does not change significantly when only particle flow rate is changed (Fig. 5b). In the latter case, the variations of ±0.5 m/s among the profiles are due to instabilities in the utility air pressure. Number densities obtained from LDA measurements by using Eq. (1) are presented in Fig. 6. Fig. 6a displays evolution of number density profile in the jet with increasing air flow rate when level of particle flow rate is kept constant. At runs 1–3 corresponding to laminar regime, the particles are concentrated within an annular region at around r/r0 = 0.5–0.7 mm. After the transition to turbulent regime the number densities homogenize. As the air flow rate is further increased, the concentrations decrease due to dilution by air and at the axial position under consideration, the jet enlarges due to the influence of turbulence on jet development. The variation of particle number density profiles with increasing particle load at Reynolds number around 4000 is presented in Fig. 6b. It is observed that as the particle load is increased above a certain threshold, the particles are drifted outwards resulting in a high density annular region. This non-homogeneous density profile is maintained in the turbulent high particle load cases but the radius and width of this concentrated ring is larger when compared to laminar case because of larger jet diameter. The ratio of ring thickness to jet radius is observed to
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be nearly the same in both regimes, i.e., 0.6 in laminar case, 0.55 in turbulent case. There are various possible causes for concentrated annular regions which are observed for particle loads higher than fv = 6 ppm in both laminar and turbulent cases. The two-phase flow within the pipe can be considered as vertical, fully developed, dilute phase, pneumatic conveying regime. The governing equations for this kind of flow indicate that the radial particle concentration distribution is dependent on electrostatic interactions and particles tend to concentrate near the pipe walls if the electrostatic charge carried by each particle is significant [12]. As the pipe material is plastic and the particles are ZrO2 which has a high dielectric constant, effects of electrostatic charging are expected to prevail within the pipe so that the particle density distribution is non-homogeneous at the pipe exit. Within the jet, particle dispersion takes place depending upon the Reynolds number and particle concentration. The reason for the concentrated ring structure measurements at high particle load conditions is that, dispersion of particles up to the measurement location at 1.2D axial position is not adequate to homogenize the initial heterogeneous distribution at the pipe exit. Another factor can be due to the dynamics within the jet, i.e., at high
particle concentrations the particles can be drifted towards the jet boundaries due to lower velocities in this region. Such concentrated annular regions in particle-laden free jets were also observed by Pothos and Longmire [13]. Measured profiles indicate that present methodology used to extract particle concentration information from LDA data provides physically reasonable local number density measurements. In an attempt to assess the reliability of the number density measurements, cross-sectional average of measured profiles are compared with estimated number densities based on the hypothetical cases of different detectable particle size ranges, as defined in Section 3.3. Fig. 7a shows the variation with Reynolds number for constant particle load and variable air flow rate and Fig. 7b displays variation of number densities with particle load for constant Re around 4000. As can be seen from the figures, measurements and estimates follow similar trends of variation but the absolute values of estimates are strongly dependent on the polydisperse nature of particles and detectable particle size range. The slightly steeper slope in Fig. 6a for the estimates of laminar runs when compared with the slope in turbulent cases is due to slightly different particle flow rates caused by void fraction difference in the seeder powder reservoir for laminar and turbulent regimes. The assumption of monodisperse particles (MD) results in significant difference between measurements and estimates. Consideration of the complete particle size distribution (PD1) results about 4 orders of magnitude more particles than measurements. This is due to the fine tail of the psd which is counted in the estimate but actually can not be detected in the measurement. In order to get an indication on the size of the particles visible to the LDA system, the size distribution range was narrowed gradually around dp/df = 1 as explained in Section 3.3. PD2 results are about an order of magnitude greater than the measurements. As the detectable particle diameter range gets narrower towards PD3 case, the number density estimates decrease and PD4 case produces estimates in favorable agreement with measurements. This outcome suggests that the detectable particle size window for the LDA system and the seeding material under consideration is 0.93 < dp/df < 1.15. 5. Practical significance
Fig. 7. Variation of measured and estimated number densities with flow conditions: (a) effect of Reynolds number; (b) effect of particle flow rate.
The methodology investigated in this study can be used to access local particle number density information in multiple phase flows from conventional LDA measurements without calibration or hardware extension. The method is found to be useful as a simple approach for relative concentration measurements. The results suggest that the size range of particles that can be counted by LDA is limited around particle size to fringe spacing ratio of unity and therefore reliable absolute concentration measurements are possible if the particles have narrow size distribution within this range.
I. Ayrancı et al. / Experimental Thermal and Fluid Science 31 (2007) 839–847
6. Conclusion A practical methodology for measurement of local particle number densities by using laser Doppler anemometry was studied on a vertical air jet seeded with controlled particle and air flow rates. Similar trends with estimates indicate that the present approach is applicable for measurement of local particle concentration and it can be used for relative measurements. The absolute LDA measurements are highly sensitive to the detectable particle size range and the size distribution of the sample particles. In order to make reliable absolute particle concentration measurements with LDA, it is important to apply this technique to particle populations with narrow size distribution around a particle diameter equal to the fringe spacing. Otherwise, a certain portion of the particles may become invisible to the detector. Present methodology is a simple and practical option for determination of particle concentration in particle-laden flows but necessitates prudent interpretation in terms of detectable particle size range. The number densities measured by this method represent local concentrations of particles of about the same size as fringe spacing. Acknowledgements Isßıl Ayrancı was supported by a French government scholarship granted by the Embassy of France in Turkey within the frame of a joint PhD program co-supervised by METU and INSA de Lyon. This study was partially supported by the French Ministry of Research (Re´seau de Recherche et d’Innovation Technologique: ‘‘Recherche Ae´ronautique sur le Supersonique’’, de´cision no. 03T233). References [1] J. Chaouki, F. Larachi, M.P. Dudukovic, Noninvasive tomographic and velocimetric monitoring of multiphase flows, Industrial & Engineering Chemistry Research 36 (11) (1997) 4476–4503.
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[2] S. Shao, Study of the flow behavior of multiphase system using laser Doppler anemometry (LDA), PhD Thesis, Illinois Institute of Technology, 1996. [3] F. Durst, A. Melling, J.H. Whitelaw, Principles and Practice of Laser Doppler Anemometry, Academic Press, London, 1981. [4] H.-E. Albrecht, M. Borys, N. Damaschke, C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques, Springer, Germany, 2003. [5] J.Y. Tu, C.A.J. Fletcher, Y.S. Morsi, W. Yang, M. Behnia, Numerical and experimental studies of turbulent particle-laden gas flow in an in-line tube bank, Chemical Engineering Science 53 (2) (1998) 225–238. [6] K. Sekoguchi, M. Takeishi, H. Kano, K. Hironaga, T. Nishiura, The measurement and calculation of furnace flow properties, in: 1st International Symposium on Application of Laser Anemometry to Fluid Mechanics, Lisbon, Portugal, 1982, Paper 16.1. [7] V. Mathiesen, T. Solberg, B.H. Hjertager, An experimental and computational study of multiphase flow behavior in a circulating fluidized bed, International Journal of Multiphase Flow 26 (3) (2000) 387–419. [8] Z. Yu, A.C. Rasmuson, Projected area of measurement volume in phase-Doppler anemometry and application for velocity bias correction and particle concentration estimation, Experiments in Fluids 27 (2) (1999) 189–198. [9] H.H. Qiu, M. Sommerfeld, A reliable method for determining the measurement volume size and particle mass fluxes using phaseDoppler anemometry, Experiments in Fluids 13 (6) (1992) 393– 404. [10] N. Huber, M. Sommerfeld, Characterization of the cross-sectional particle concentration distribution in pneumatic conveying systems, Powder Technology 79 (3) (1994) 191–210. [11] H.E. Albrecht, M. Borys, W. Fuchs, The cross-sectional area difference method – a new technique for determination of particle concentration by laser-Doppler anemometry, Experiments in Fluids 16 (1) (1993) 61–69. [12] L.-S. Fan, C. Zhu, Principles of gas–solid flows, in: A. Varma (Ed.), Cambridge Series in Chemical Engineering, Cambridge University Press, UK, 1998, p. 482. [13] S. Pothos, E.K. Longmire, Control of a particle-laden jet using a piezo-electric actuator, in: 11th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 2002.