Tutorial / Correlation Image Velocimetry: optimisation of parameters

To improve the results, come back to the GUI CIV, and follow these successive steps, corresponding to a sequence of operations.

The main PIV parameters

The first parameter to adjust is the time interval between images, which should be sufficiently long to provide a displacement of a few pixels. The measurement precision is typically 0.2 pixel, so that a displacement of 4 pixels, as in the example, provides a relative precision of 5 %. A larger displacement would be preferable in terms of precision but may yield to poor image correlation and ’false vectors’.

Once the image pair has been chosen, the main parameters are the size of the correlation box in both directions ([num_CorrBoxSize]_1] and _2) and the size of the search box, ([num_!SearchBoxSize_1] and _2), expressed in pixels. For each velocity vector, the correlation box is moved within the search box to optimise the image correlation between the two sub-images inside the correlation box. To allow for a displacement of d pixels, the search box size must exceed the correlation box by at least d+2 on both sides, so 2d+4. A systematic shift [num_!SearchBoxShift_1], and _2, can be also introduced to minimise the search area in the presence of a mean flow.

The parameter [num_CorrSmooth] is used to fit the correlation data with a smooth function to obtain the maximum with sub-pixel precision. We generally keep the default value 1.

The parameters [num_Dx] and [num_Dy] define the mesh of the measurement grid, in pixels. Reduce them to get more vectors, but keep in mind that the spatial resolution is limited by the size of the correlation box.

The PIV operation is conveniently visualised by pressing the button [!TestCiv1] in the GUI civ. Then the image appear in a new GUI view_field, in which the mouse motion displays the correlation function, which appears in a secondary window, see figure. The resulting vector is shown as a line pointing to the correlation maximum. The corresponding correlation and search boxes are shown in the image. Let us run again PIV with [CorrBoxSize]=[25 25] and [SearchBoxSize]=[33,33], limiting ourselves to CIV1, and visualisae the result with uvmat. Many black vectors (F=-2) are obtained, showing that the search domain is too small, so that the correlation maximum is constrained by the limited search interval. Repeat the operation with [SearchBoxSize]=[35,33], then the arrows are not black anymore.

* Optimizing the Civ1 parameters: Select the [CIV1] check box so the corresponding parameters show up. Improve the spatial resolution by selecting smaller correlation boxes in the civ1 menu, for instance [Bx],[By] to 19 and 13 (image pixels). This is possible because of the good image quality and high particle density. The use of a smaller box in y allows to optimize the resolution in this direction, to deal with the strong vertical shear. It is now possible to adjust the search range, using knowledge on extremal velocities, see histograms displayed by uvmat in phys coordinates. We introduce estimated bounds on each velocity component, [min] to -2 and [max] to 6 for ’u’ and (-3, 3) for ’v’, and press the button [Search Range]. The optimum search ranges and shifts are now displayed. In consistency with higher resolution, we set the grid mesh to [Dx] and [Dy] to 10. Finally select the Mask option : the mask name should be displayed in the corresponding edit box, else a browser leads to the appropriate mask file.

* FIX1: Select the ’FIX1’ operation, which eliminates some false vectors using several criteria. Use the default parameters.

* PATCH1: Select the ’PATCH1’ operation, to interpolate the vectors on a regular grid and calculate spatial derivatives. Choose the default value 10 for the smoothing parameter [FieldSmooth]. You can later try different values, the smoothing effect increasing with FieldSmooth. Keep the default values for the other parameters.

* CIV2: Select the ’CIV2’ operation to improve the correlation results, using the information on local image deformation, provided by the previous knowledge on velocity spatial derivatives (calculated in patch1). Use a finer grid dx= dy=5 than for civ1. The spatial resolution can be slightly improved by decreasing the correlation box, using for instance Bx,By=(15,11). The shift of the search range is here given at each point by the prior estimate from Civ1, so that the search range can be optimized: choose [21,17] which provides a margin of 3 pixels on each side of the correlation box. Note that ’civ2’ corresponds to a new measurement from the images, the previous civ1 and patch1 operations being used only as an initial guess for the search of optimal correlations.

Then select ’FIX2’ and ’PATCH2’ with the default parameters.

* Running the calculation: Press [RUN] to run the calculation. The results are stored in a new subdirectory, CIV_1, so the previous results are not erased (you can also set the name of the subdirectory in the GUI, by the edit boxes [SubDirCiv1] and [SubDirCiv2]. The existing subdirectories are listed above.

The status of the calculation is displayed in a new window which refreshes automatically. Close it to avoid blocking of new Matlab operations. This status window can be opened again by pushing the button [STATUS] in the GUI civ. Do not close civ until the calculation is finished.

The parameters of a CIV computation are stored in a xml file with extension ..CivDoc.xml created in the directory containing the velocity files. These parameters can retrieved, opening this xml file with the browser of the GUI civ. Then the image file itself needs to be opened (the select again the check boxes for the operations beyond civ1 hidden by default).

The result can be improved again by performing a third civ iteration, civ3. For that purpose, select only the ’civ2’, ’fix2’ and ’patch2’ operations with the same parameters as previously. The previous result is now considered as ’civ1’, so set CIV as the subdirectory in the edit window [SubDirCiv1]. Select a new subdirectory name, for instance ’CIV3’ in the edit window [SubDirCiv2]. Further iterations could be similarly performed, but the improvement becomes negligible.

The following figure shows the final vorticity field, in which the vorticity roll up in the wake of the sphere is clearly visible. A zoom near a vortex shows the vorticity superposed with velocity vectors.