Practical Implementation of Technique

ration; by tailoring the position, quantity, and spacing of the measurement planes, the technique can be put to a great many uses, over a wide range of flow phenomena. This section presents an overview of potential applications, along with other practicalities that must be considered in any experimental setup.

6.4.1

Potential uses of MP-VSE

Clearly, the ability to produce instantaneous 3-dimensional, 3-component ve- locity data lends itself to many applications, although it must be remembered that the results are predictions, rather than a measurement of the flow. Un- fortunately this precludes use of MP-VSE for a number of tasks that would be possible with true volumetric measurements, particularly when the accurate measurement of statistical quantities is sought. Instead, the strength of MP- VSE is likely to be found in the study of coherent structures. The results from the previous section confirm its potential to accurately characterise the domi- nant flow structures in both the predicted velocity and vorticity fields. Also, as a form of stochastic estimation, MP-VSE lends itself naturally to many of the applications commonly found in this field, with the obvious benefit of providing a full 3D-3C reconstruction. In particular, the reconstructed veloc- ity fields could potentially provide the basis for subsequent low-dimensional analysis and modelling using POD.

6.4.2

Temporal response

One aspect of MP-VSE not yet considered is the temporal response. For time- stationary flows, the rate at which predictions can be made is limited by the speed at which successive Q plane measurements can be acquired. Hence, with high-speed cameras and/or slow moving flows, the ability to make time- resolved volumetric predictions may be possible. As explained in section 6.3, there is an inherent difficulty producing predictions at multiple points in time for non-stationary flows, as a separate prediction model must be made for each time of interest. As such, MP-VSE is poorly suited for time-resolved predic- tions of non-stationary flows; even with the availability of high-speed cameras, the data and processing requirements to produce the prediction models would quickly become prohibitive.

6.4.3

Practical limitations to volume

Although it is unable to rival the accuracy of existing 3D-3C measurement techniques, MP-VSE does offer some unique advantages. Perhaps most impor- tantly, neither the size nor resolution of the reconstructed volume are subject to the same limitations as other techniques (as discussed in section 2.2). The ability to predict large volumes is due to the extensibility of the technique, whereby the size of the volume can be increased with the addition of further

Q planes. A wide variety of multiple plane PIV approaches exist (see section 2.2), which all have the potential to be used for MP-VSE, but each config- uration appears to have an upper limit of the number of planes that can be measured in practice. Furthermore, the increase in the number of planes is likely to correspond to a increase in the cost of the equipment required. As such, there will always be an upper limit to the size of volume that can be

predicted.

Choice of number and positions of Q planes

A second, no less important limitation to the size of the prediction volume is due to the flow itself. Accurate prediction of the flow requires that the conditional vectors are well correlated with at least some of the unconditional vectors. Regardless of the flow in question, it can be expected that the corre- lation between two points will ultimately decrease as their separation becomes larger. Generally speaking, given a finite number of Qplanes, it is likely that the accuracy of prediction will drop as the volume of interest is increased, and the spacing between the Q planes becomes larger. Conversely, a reduction in volume should be accompanied by an increase in accuracy.

Even though this effect serves to place a limit on both the volume and accuracy of MP-VSE, the ability to easily trade one for the other, and hence adapt the setup for the particular application, highlights the flexibility of the approach. For any given application, however, an appropriate choice for the number and position of Q planes will have to be made with regard to the behaviour of the flow. As a minimum requirement, some knowledge of structure size or correlation length would be necessary to make an informed decision on the spacing of the planes, and to provide an indication of the resulting predictive power. However, a more rigorous approach to Q plane positioning can be achieved if preliminary PIV measurements of the P plane are available first. As shown in section 6.2, the MP-VSE prediction model is derived from theP plane measurements, in a progress that begins by specifying the vectors in theP plane that correspond to the intersection of theQplanes. With this in mind, prediction models can be build from the preliminary P

plane measurements withQplanes in varying positions. Then, in the same way that cross validation is used to assess the relative performance of competing regression models, it can be applied to compare the prediction accuracy of the different Qplane configurations. Viewed in this light, the task of Q plane positioning is a straightforward mathematical optimisation problem where the aim is to maximise prediction accuracy, which is a function of the Q plane coordinates. In practice, this maximisation could achieved though any number of approaches, ranging from simple trial-and-improvement, through to a fully automated numerical optimisation.