Integration of non-time-resolved PIV and time-resolved velocity point sensors for dynamic estimation of time-resolved velocity fields

We demonstrate a three-step method for estimating time-resolved velocity fields using time-resolved point measurements and non-time-resolved particle image velocimetry (PIV) data. First, we use linear stochastic estimation to obtain an initial set of time-resolved estimates of the flow field. These initial estimates are then used to identify a linear model of the flow physics. The model is incorporated into a Kalman smoother, which is used to make a second, improved set of estimates. We verify this method with an experimental study of the wake behind a 7.1% thick elliptical-leading-edge flat plate at a chord Reynolds number of 50,000. Time-resolved PIV data are acquired synchronously with a point measurement of velocity. The above method is then applied to a non-time-resolved subset of the PIV data, along with the time-resolved probe signal. This produces a time-resolved, low-dimensional approximation of the velocity field. The original, time-resolved PIV snapshots are then used to compare the accuracy of the initial, stochastic estimates to the latter, dynamic ones, as measured by the kinetic energy contained in the estimation errors. We find that, for this particular flow, the Kalman smoother is able to utilize the dynamic model and the non-time-resolved PIV data to produce estimates that are not only more accurate, but also more robust to noise. Consequently, modal decompositions based on these estimates more accurately identify coherent structures in the flow.

[1]  Yann Guezennec,et al.  An application of the stochastic estimation to the jet mixing layer , 1992 .

[2]  Mark N. Glauser,et al.  Stochastic estimation and proper orthogonal decomposition: Complementary techniques for identifying structure , 1994 .

[3]  A. Naguib,et al.  Stochastic estimation and flow sources associated with surface pressure events in a turbulent boundary layer , 2001 .

[4]  Joseph H. Citriniti,et al.  Examination of a LSE/POD complementary technique using single and multi-time information in the axisymmetric shear layer , 1999 .

[5]  Nathan E. Murray,et al.  Modified quadratic stochastic estimation of resonating subsonic cavity flow , 2007 .

[6]  Yann Guezennec,et al.  Stochastic estimation of coherent structures in turbulent boundary layers , 1989 .

[7]  Nathan E. Murray,et al.  Estimation of the flowfield from surface pressure measurements in an open cavity , 2003 .

[8]  Clarence W. Rowley,et al.  Koopman spectral analysis of separated flow over a finite-thickness flat plate with elliptical leading edge , 2011 .

[9]  J. Westerweel,et al.  Universal outlier detection for PIV data , 2005 .

[10]  Kelly Cohen,et al.  A heuristic approach to effective sensor placement for modeling of a cylinder wake , 2006 .

[11]  Ronald Adrian,et al.  Stochastic Estimation of Conditional Structure: a Review , 1994 .

[12]  Ronald Adrian,et al.  On the role of conditional averages in turbulence theory. , 1975 .

[13]  J. Westerweel,et al.  Efficient detection of spurious vectors in particle image velocimetry data , 1994 .

[14]  H. K. Moffatt.  Stochastic Tools in Turbulence. By J OHN L. L UMLEY . Academic Press, 1970. 205 pp. $5.60. Turbulence Phenomena. By J. T. D AVIES . Academic Press, 1972. 412 pp. $19.50. , 1975 .

[15]  Mathieu Legrand,et al.  Flow temporal reconstruction from non-time-resolved data part I: mathematic fundamentals , 2011 .

[16]  Mia Hubert,et al.  An adjusted boxplot for skewed distributions , 2008, Comput. Stat. Data Anal..

[17]  Clarence W. Rowley,et al.  Reduced-order models for control of fluids using the eigensystem realization algorithm , 2008, 0907.1907.

[18]  Ronald Adrian,et al.  Higher‐order estimates of conditional eddies in isotropic turbulence , 1980 .

[19]  Jonathan W. Naughton,et al.  Multi-time-delay LSE-POD complementary approach applied to unsteady high-Reynolds-number near wake flow , 2010 .

[20]  John B. Moore,et al.  Optimal State Estimation in High Noise , 1968, Inf. Control..

[21]  Qi Song,et al.  Dynamic Surface Pressure Based Estimation for Flow Control , 2008 .

[22]  Charles E. Tinney,et al.  On spectral linear stochastic estimation , 2006 .

[23]  C. Rowley,et al.  Modeling of transitional channel flow using balanced proper orthogonal decomposition , 2007, 0707.4112.

[24]  L. Sirovich.  Turbulence and the dynamics of coherent structures. II. Symmetries and transformations , 1987 .

[25]  Dan Simon,et al.  Optimal State Estimation: Kalman, H∞, and Nonlinear Approaches , 2006 .

[26]  I. Mezić,et al.  Spectral analysis of nonlinear flows , 2009, Journal of Fluid Mechanics.

[27]  Yassin A. Hassan,et al.  Approximation of turbulent conditional averages by stochastic estimation , 1989 .

[28]  Stochastic estimation and proper orthogonal techniques for identifying structure , 1994 .

[29]  Todd Schultz,et al.  Application of multivariate outlier detection to fluid velocity measurements , 2010 .

[30]  P. Schmid,et al.  Dynamic mode decomposition of numerical and experimental data , 2008, Journal of Fluid Mechanics.

[31]  Clarence W. Rowley,et al.  Model Reduction for fluids, Using Balanced Proper Orthogonal Decomposition , 2005, Int. J. Bifurc. Chaos.

[32]  Mark N. Glauser,et al.  Towards practical flow sensing and control via POD and LSE based low-dimensional tools , 2004 .

[33]  Mathieu Legrand,et al.  Flow temporal reconstruction from non time-resolved data part II: practical implementation, methodology validation, and applications , 2011 .

[34]  Parviz Moin,et al.  Stochastic estimation of organized turbulent structure: homogeneous shear flow , 1988, Journal of Fluid Mechanics.

[35]  Nathan E. Murray,et al.  An application of Gappy POD , 2006 .

[36]  L. Sirovich.  Turbulence and the dynamics of coherent structures. I. Coherent structures , 1987 .

[37]  P. Holmes,et al.  Turbulence, Coherent Structures, Dynamical Systems and Symmetry , 1996 .