100084, People's Republic of China Published online: 07 May 2010.

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1 This article was downloaded by: Tsinghua University] On: 09 September 205, At: 00: Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered umber: Registered office: 5 Howick Place, London, SWP WG Journal of Hydraulic Research Publication details, including instructions for authors and subscription information: Bias errors induced by cross-talk in two-phase flow measurements Danxun Li a, Xingkui Wang a & Qiang Zhong a a State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing, 00084, People's Republic of China Published online: 07 May 200. To cite this article: Danxun Li, Xingkui Wang & Qiang Zhong (200) Bias errors induced by cross-talk in two-phase flow measurements, Journal of Hydraulic Research, 48:2, , DOI: 0.080/ To link to this article: PLEASE SCROLL DOW FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the Content ) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at

2 Journal of Hydraulic Research Vol. 48, o. 2 (200), pp doi:0.080/ # 200 International Association for Hydro-Environment Engineering and Research Research paper Bias errors induced by cross-talk in two-phase flow measurements DAXU LI, Dr, Associate Professor, State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing, 00084, People s Republic of China. lidx@tsinghua.edu.cn (author for correspondence) Downloaded by Tsinghua University] at 00: 09 September 205 XIGKUI WAG, Professor, State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing, 00084, People s Republic of China. wangxk@tsinghua.edu.cn QIAG ZHOG, PhD candidate, State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing, 00084, People s Republic of China. zhongq09@mails.tsinghua.edu.cn ABSTRACT Cross-talk was identified as an important elemental uncertainty source in dispersed two-phase flow measurement with laser-doppler anemometry or particle tracking velocimetry. Analytical formulations are presented to quantify the cross-talk bias errors introduced to the ensemble-averaged mean and root-mean-square (rms) velocities. Experimental data available in the literature were used to demonstrate the possible unintended consequences of these errors. It was found that these cross-talk errors are closely related to the slip velocity between the two phases. The error in the mean velocity is proportional to the cross-talk ratio times the slip velocity. The error in the rms velocity depends on the rms velocities of each phase, the cross-talk ratio, and the slip velocity. In practice, the presence of cross-talk may lead to either under- or overestimation of the true velocities. Keywords: Bias error, cross-talk, turbulence, two-phase flow, velocity Introduction In most two-phase flow tests, the measurement of the carrier phase velocity is made by seeding and sampling tracer particles in the flow. The tracers may have similar geometrical, dynamic, or light-scattering properties as the discrete phase, and crosstalk, or misidentification of signals from one phase or the other, is likely to occur. The cross-talk problem first drew attention when researchers began to apply traditional laser-doppler anemometry (LDA) to two-phase flow measurements (Lee and Durst 982, Modarress et al. 984). Recent studies conducted with particle tracking velocimetry (PTV) and particle image velocimetry (PIV) resurfaced its significance (Muste et al. 2005). Although various techniques have been used to improve the effectiveness of phase discrimination in LDA (Qiu et al. 99, Muste et al. 996, 998) and PIV/PTV (Kiger and Pan 2000, Poelma et al. 2006, Zhang et al. 2008), the crosstalk effect cannot be completely eliminated in cases where the density of the solid phase is relatively high (Modarress et al. 984) or the tracer and the dispersed phase are not well separated in size distribution (Zoltanic and Bicen 990, Qiu et al. 99). The cross-talk effects on measured mean and root-meansquare (rms) velocities have been identified and quantified in only few experiments. Modarress and Tan (983) reported an increase in the measured mean velocity of the air phase in solid gas flows where the solid phase velocity is 32% higher than that of the gas phase. Kulick et al. (994) observed enhancement of the rms velocity due to the effect of cross-talk, and claimed that cross-talk error can serve only to increase the measured gas-phase turbulence intensity. Evaluating the cross-talk error is of practical importance to report measurement accuracy (Park and Ghent 989) or helps to set experimental parameters, such as the upper limit of solid density (Jakobsen et al. 996). This research presents theoretical analysis of the cross-talk bias errors introduced to the mean and rms velocities. Experimental evidence is also given. Revision received 30 October 2009/Open for discussion until 3 October 200. ISS print/iss online 250

3 Journal of Hydraulic Research Vol. 48, o. 2 (200) Bias errors induced by cross-talk in two-phase flow measurements 25 2 Bias error in mean velocity 2. Analytical formulation In two-phase flow tests, the measured mean (subscript m) velocity for the target phase U m is calculated as U m = i= U i () a = b DU U f (7) Equation (7) indicates that the cross-talk error in the mean velocity increases linearly with the cross-talk ratio as well as the slip velocity. Downloaded by Tsinghua University] at 00: 09 September 205 where is the number of sampled instantaneous velocities and U i is the ith instantaneous velocity. If cross-talk occurs, the sampled velocities include a number of contamination data that leak into the target phase (denoted by f) from the other phase (denoted by p). Suppose the number of real and contamination instantaneous velocities are n and n 2 with n + n 2 ¼, respectively, then Eq. () can be re-written as ( ) U m = n U fi + n 2 U pi i= where U fi and U pi are the ith instantaneous velocities of the two phases, respectively. Define the cross-talk ratio as b ¼ n 2 /, such that Eq. (2) is transformed to U m = n U f + n 2 U p i= (2) =( b)u f + bu p (3) where U f and U p are the mean velocities of two phases, respectively. ote that these are determined based on n and n 2, respectively, and they are free from cross-talk errors. Equation (3) simply states that the measured mean velocity at the presence of cross-talk is the weighted average of the mean two-phase velocities. Define slip velocity as the difference in mean velocity between the two phases Substituting Eq. (4) into Eq. (3) yields DU = U p U f (4) U m = U f + bdu (5) If cross-talk occurs, the measured mean velocity deviates from its true value by a product of the cross-talk ratio times the slip velocity. If DU. 0, the mean velocity is overestimated by the measurement; if DU, 0, the mean velocity is underestimated, however. Let the relative magnitude of the cross-talk error be Substituting Eq. (5) into Eq. (6) yields a = U m U f (6) 2.2 Experimental evidence Available experimental data are in good agreement with Eq. (7) in evaluating the cross-talk error for the mean velocities. The quantification of such errors is rather simple and straightforward, therefore. For example, Park and Ghent (989) reported that a 30% cross-talk ratio and a 50% slip velocity resulted in a 5% uncertainty in the mean velocity of the gas phase. Equation (7) leads to exactly the same result, as b ¼30% and DU/U f = 50% yields a ¼ 5%. 3 Bias error in rms velocity 3. Analytical formulation The measured rms velocity u m is calculated as This is equivalent to u m = ( ) ] /2 2 U i U m (8) u m = n ( ) 2+ n 2 ( ) ] /2 2 U fi U m U pi U m (9) Substituting Eq. (5) into Eq. (9) yields ( u m = ) /2 n (U fi U f bdu) 2 + n 2 (U pi U f bdu) 2 ] /2 (0) The first term in the brackets of Eq. (0) can be developed into n ( ) 2 U fi U f bdu = n ( ) 2 2bDU n U fi U f ( ) U fi U f + n b 2 (DU) 2 ()

4 252 D. Li et al. Journal of Hydraulic Research Vol. 48, o. 2 (200) It is evident that n Substituting Eq. (2) into Eq. () yields ( ) U fi U f = 0 (2) The tests by Kulick et al. (994) belong to this category. But if u p u f and the slip velocity is negligibly small, Eq. (8) may yield a measured rms velocity less than the true value, resulting in an underestimation of true turbulence. Let the relative magnitude of the cross-talk error in rms velocity be n ( ) 2= n U fi U f bdu ( ) 2+n U fi U f b 2 (DU) 2 (3) a 2 = u m u f Substituting Eq. (8) into Eq. (9) yields (9) Downloaded by Tsinghua University] at 00: 09 September 205 Similarly, one obtains n 2 ( ) 2 n 2 U pi U f bdu = = n 2 ] 2 U pi U p ( b)du ( ) 2+n2 U pi U p ( b) 2 (DU) 2 (4) Substituting Eqs. (3) and (4) into Eq. (0) and simplifying yields u m = n ( ) 2+ n 2 ( ) ] /2 2+b( b)(du) 2 U fi U f U pi U p (5) ote that the first two terms in Eq. (5) represent the rms velocities (free from cross-talk errors) of the two phases, respectively, i.e. n n 2 ( ) 2= n U fi U f u f 2 =( b)u f (6) 2 ( ) 2= n 2 U pi U p u 2 p =bu 2 p (7) where u p and u f are rms velocities for the two phases, respectively. ote that u p and u f are based on n and n 2, free from cross-talk errors. Substituting Eqs. (6) and (7) into Eq. (5) yields the measured rms velocity at the presence of cross-talk u 2 m = ( b ) ( ) ] /2 u 2 +b b ( DU) 2 (8) f +bu 2 p Equation (8) indicates that the measured rms velocity depends not only on the calculated rms velocities of each phase but also on the slip velocity. ote that the third term in Eq. (5) is always positive, so that the slip velocity increases the measured rms velocity under cross-talk. In practical tests where u p, u f and DU are of the same order of magnitude, the actual turbulence level is likely to be overestimated due to the cross-talk effect. ]/2 a 2 = ( b)+b(u p /u f )2 + b( b)(du/u f )2 (20) Equation (20) involves four parameters to evaluate a 2, namely the rms velocities of each phase, the slip velocity, and the cross-talk ratio. To give a rough estimate of the magnitude of a 2, consider a simplified hypothetical case in which DU = u p = u f Z. Then, Eq. (20) reduces to a 2 = + b( b) ] /2 (2) Equation (2) yields a 2 ¼ 0.5%, 2.3%, 4.4% for b ¼ 0.0, 0.05, and 0., respectively. Errors of such a magnitude are comparable to commonly reported magnitude of turbulence modification in sediment-laden flows, and need to be carefully accounted for. 3.2 Experimental evidence To date, experimental data that thoroughly investigate the crosstalk errors in rms velocities are lacking. That is partly due to the difficulties in obtaining complete information required by Eqs. (9) and (20). Here two data sets presented by Muste et al. (2005) are used to illustrate the characteristics of a 2 under various combinations of b, p /u f, and DU/u f. Following is a brief description of the experiment. The tests included two sets of measurements, one set with natural sand (S2, specific gravity ¼ 2.65) and the other set with neutrally buoyant sediment (BS2, specific gravity ¼.02). In each test, a two-phase flow perspective was adopted and simultaneous yet discrete measurement of the liquid and solid phase motions was made to compute the mean and rms velocities of each phase. ote that the cross-talk effect in the original measurement can be ignored as the particle is much larger in size than the fluid particle. But treating the measured data with a mixed-flow perspective, i.e. putting together all velocity samples from both phases, is equivalent to a two-phase test that allows solid particles to leak freely into the liquid phase during the test. Thus, the mixed-flow processing of data provides a hypothetical case in which man-made cross-talk errors occur. Figure shows the cross-talk error a 2 across the entire water depth together with other relevant test information, including (a)

5 Journal of Hydraulic Research Vol. 48, o. 2 (200) Bias errors induced by cross-talk in two-phase flow measurements Discussion of results Downloaded by Tsinghua University] at 00: 09 September 205 Figure Variation of a 2 and its factors (data from Muste et al. 2005): (a) cross-talk ratio, (b) rms velocity ratio, (c) ratio of slip velocity to rms velocity, and (d) cross-talk error in rms velocity cross-talk ratio b, (b) ratio v p /v f of measured rms velocities in vertical direction, and (c) ratio of measured velocity lag to rms velocity DV/v f. ote that a 2 is calculated using Eq. (9) based on measured rms-velocities. For S2, the velocity lag is relatively large, i.e. DV = O(v f ). The b values cover a wide range from zero in the region near water surface to over 20% in the region immediately above the channel bed. The distributions of v p /v f and DV/v f are relatively uniform along the vertical, i.e. v p /v f =.2.4 and DV/v f = Thus b plays a major role in determining the cross-talk error. Figure shows that a 2 and b for S2 are similar along the vertical, i.e. both decrease with the distance above the channel bed. The value of a 2. 0 across the entire water depth, indicating that the actual turbulence level is overestimated due to the cross-talk effect. The maximum of a 2 is over 0% in the near bed region. For BS2 with neutrally buoyant sediment, the velocity lag is negligibly small, i.e. DV /v f 0. The distribution of b is much more uniform than that of S2, such that v p /v f becomes the most prominent factor in determining the cross-talk error. The profiles of a 2 and v p /v f for BS2 vary similarly along the vertical. ote that a 2 is less than zero if y/h, 0.2, where y is the distance above channel bed and h is the water depth, increasing to above zero for y/h. 0.2, thereby implying that the cross-talk error may lead to either over- or underestimation of the actual turbulence. This finding is apparently inconsistent with observations in gas solid two-phase flows for which cross-talk error can serve only to increase the measured gas-phase turbulence intensity (Kulick et al. 994). In commonly encountered sediment-laden flows, the slip velocity is generally of the same order as the rms velocity but far less than the mean velocity of the water flow (Muste et al. 2005). Thus the cross-talk error in the mean velocity can be safely neglected except in the vicinity of the channel bed, but the error in the rms velocity can be significant and may lead to false interpretation of test data. For instance, the hardly tangible effect of suspended particles on turbulence modification can be easily masked by cross-talk errors. Muste (2002) examined a list of sources of bias errors in sediment-laden flow measurement that may result in inconsistent or even contradictory results with respect to the effect of suspended particles on water flow. The cross-talk error should be added to that list and needs to be evaluated with reference to uncertainty assessment standards and guidelines, such as ASME PTC (ASME 2005). Past investigations on two-phase flows usually adopted a mixed-flow perspective, yielding velocity and concentration profiles without distinguishing between the two phases (Best et al. 997, Cellino and Graf 2000, Graf and Cellino 2002). The approach of treating the flow as a mixture of water and suspended particles is equivalent to a true two-phase measurement that is subjected to cross-talk errors. A thorough estimate of the cross-talk errors helps to increase the usefulness of previous findings and facilitates communications between mixed-flow and two-phase perspectives. 5 Conclusions Cross-talk is an important elemental uncertainty source in dispersed two-phase flow measurements. This research first quantifies these bias errors introduced to the ensemble-averaged mean and rms velocities. Experimental evidence is also given. If cross-talk occurs, the mean velocity deviates from its true value by a product of the cross-talk ratio times the slip velocity, with the deviation in the rms velocity depending on the true rms velocities of each phase, the cross-talk ratio, and the slip velocity. The cross-talk effect may lead to either over- or underestimation of the true velocities at various combinations of parameters. The mixed-flow approach of measuring sediment-laden flow was demonstrated to follow two-phase measurement subjected by cross-talk errors. The analysis of cross-talk errors provides a bridge connecting mixed-flow and two-phase flow perspectives. Acknowledgements The authors are deeply grateful to Dr Muste, Iowa Institute of Hydraulic Research, for providing his experimental data used in plotting Fig.. Financial support by SFC ( ) is acknowledged.

6 254 D. Li et al. Journal of Hydraulic Research Vol. 48, o. 2 (200) Downloaded by Tsinghua University] at 00: 09 September 205 otation h ¼ entire water depth n, n 2, ¼ number of velocity samples for target phase, contamination phase, and both phases U i ¼ ith instantaneous velocity U m,u f,u p ¼ mean velocities of mixture, water phase, and particles u m, u f, u p ¼ rms velocities of mixture, water phase, and particles v f, v p ¼ vertical rms velocities of water phase and particles y ¼ distance above channel bed a, a 2 ¼ magnitudes of cross-talk error in mean and rmsvelocities b = n 2 / ¼ cross-talk ratio DU ¼ slip velocity DV ¼ slip velocity in vertical direction References ASME (2005). Performance Test Code American Society of Mechanical Engineers. Test uncertainty. ew York, Y. Best, J., Bennett, S., Bridge, J., Leeder, M. (997). Turbulence modulation and particle velocities over flat sand beds at low transport rates. J. Hydraulic Eng. 23(2), Cellino, W., Graf, W.H. (2000). Experiments on suspension flow in open channels with bed forms. J. Hydraulic Res. 38(4), Graf, W.H., Cellino, W. (2002). Suspension flows in open channels: experimental study. J. Hydraulic Res. 40(4), Jakobsen, M.L., Easson, W.J., Greated, C.A., Glass, D.H. (996). Particle image velocimetry: simultaneous two-phase flow measurements. Meas. Sci. Tech. 7, Kiger, K.T., Pan, C. (2000). PIV technique for the simultaneous measurement of dilute two-phase flows. J. Fluids Eng. 22(4), Kulick, J.D., Fessler, J.R., Eaton, J.D. (994). Particle response and turbulent modification in fully developed channel flow. J. Fluid Mech. 277, Lee, S.L., Durst, F. (982). On the motion of particles in turbulent duct flows. Int. J. Multiph. Flow. 8(2), Modarress, D., Tan, H. (983). LDA signal discrimination in two-phase flows. Exp. Fluids. (), 6. Modarress, D., Tan, H., Elghobashi, S. (984). Two-component LDA measurement in a two-phase turbulent jet. AIAA J. 22(5), Muste, M. (2002). Sources of bias errors in flume experiments on suspended-sediment transport. J. Hydraulic Res. 40(6), Muste, M., Fujita, I., Kruger, A. (998). Experimental comparison of two laser-based velocimeters for flows with alluvial sand. Exp. Fluids. 24(4), Muste, M., Parthasarathy, R.., Patel, V.C. (996). Discriminator laser-doppler velocimetry for measurement of liquid and particle velocities in sediment-laden flows. Exp. Fluids. 22(), Muste, M., Yu, K., Fujita, I., Ettema, R. (2005). Two-phase versus mixed-flow perspective on suspended sediment transport in turbulent channel flows. Water Res. Res. 4(), 22. Park, C.J., Ghent, L.-D. (989). Experimental investigation of confined turbulent jets 2: Particle-laden flow data. AIAA J. 27(), Poelma, C., Westerweel, J., Ooms, G. (2006). Turbulence statistics from optical whole-field measurements in particleladen turbulence. Exp. Fluids. 40(3), Qiu, H.H., Sommerfeld, M., Durst, F. (99). High-resolution data processing for phase-doppler measurements in a complex two-phase flow. Meas. Sci. Tech. 2(5), Zhang, W., Wang, Y., Lee, S.J. (2008). Simultaneous PIV and PTV measurements of wind and sand particle velocities. Exp. Fluids. 45(2), Zoltanic, C.K., Bicen, A.F. (990). Velocity measurements in a turbulent, dilute two-phase jet. Exp. Fluids. 9(5),