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Dispersion within Emergent Vegetation Using PIV and Concentration Measurements Uri Shavit Technion, Haifa, Israel

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The advective dispersive equation The local (micro-scale) transport equation - Flow rate - Cross – section area

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1.Fickian dispersion (Concentration only) 2.Decomposition and averaging (Euler) ( Simultaneous concentration & velocity) 3.Ensemble of path-lines (Lagrange) (Velocity only) We examine the PIV ability to measure dispersion, applying the following three methods:

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The Experimental Setup

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The experimental setup:

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Visualization The experimental challenge is to measure simultaneously concentration & velocity.

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Image Pair (1) (Visualization and conc. measurements)

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Image Pair (2) (Velocimetry)

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Experimental Conditions

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whereis the injection discharge 1. Fickian Dispersion

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Time-averaged normalized concentration (following an intensive calibration). Q/A=4.58cm/s, d= 3.5%. Fickian Dispersion D [cm 2 /s]

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2. Decomposition and double averaging of the convective equation (Eulerian) Requires simultaneous measurements of velocity and concentration

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Decomposition x y Flow Considering the commutativity rules:

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The averaging end result: 0 The dispersion term

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Q=66 min -1, Array Density = 3.5% 50mm Lens 2 4 6 8 10 12 14 16 18 20 24681012141618 Y(cm) X(cm)

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200mm Lens Y(cm) X(cm)

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Spatial variations LongitudinalLateral Temporal fluctuations The calculated dispersion coefficient x y Flow

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3. An Ensemble of Path-lines (a Lagrangian approach)

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The location of a particle released at (x 0, y 0 ) at time t 0 is, Kundu, 1990, p. 324 or Williamson (1996) The Strouhal number:

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Lateral dispersion is then calculated using the mean square of the lateral variations, Where Y is:

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Q=66 min -1, Array Density = 3.5%50mm Lens, 2 4 6 8 10 12 14 16 18 20 24681012141618 Y(cm) X(cm) The Evolution of Pathlines

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The Results of the Lagrangian Approach:

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The dispersion coefficient d = 3.5%

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4 cm A Moving Frame of Reference: Q = 23 min -1, Array Density = 3.5%

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Acknowledgments: The Israel Science Foundation (ISF) Grand Water Research Institute Joseph & Edith Fischer Career Development Chair Tuval Brandon Mordechai Amir Ravid Rosenzweig

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