Dispersion within Emergent Vegetation Using PIV and Concentration Measurements Uri Shavit Technion, Haifa, Israel
The advective dispersive equation The local (micro-scale) transport equation - Flow rate - Cross – section area
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:
The Experimental Setup
The experimental setup:
Visualization The experimental challenge is to measure simultaneously concentration & velocity.
Image Pair (1) (Visualization and conc. measurements)
Image Pair (2) (Velocimetry)
Experimental Conditions
whereis the injection discharge 1. Fickian Dispersion
Time-averaged normalized concentration (following an intensive calibration). Q/A=4.58cm/s, d= 3.5%. Fickian Dispersion D [cm 2 /s]
2. Decomposition and double averaging of the convective equation (Eulerian) Requires simultaneous measurements of velocity and concentration
Decomposition x y Flow Considering the commutativity rules:
The averaging end result: 0 The dispersion term
Q=66 min -1, Array Density = 3.5% 50mm Lens Y(cm) X(cm)
200mm Lens Y(cm) X(cm)
Spatial variations LongitudinalLateral Temporal fluctuations The calculated dispersion coefficient x y Flow
3. An Ensemble of Path-lines (a Lagrangian approach)
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:
Lateral dispersion is then calculated using the mean square of the lateral variations, Where Y is:
Q=66 min -1, Array Density = 3.5%50mm Lens, Y(cm) X(cm) The Evolution of Pathlines
The Results of the Lagrangian Approach:
The dispersion coefficient d = 3.5%
4 cm A Moving Frame of Reference: Q = 23 min -1, Array Density = 3.5%
Acknowledgments: The Israel Science Foundation (ISF) Grand Water Research Institute Joseph & Edith Fischer Career Development Chair Tuval Brandon Mordechai Amir Ravid Rosenzweig