Bridging PIV spatial and temporal resolution using governing equations and development of the coaxial volumetric velocimeter

Abstract

A series of techniques is proposed for volumetric air flow measurements that are based upon the principles of particle image velocimetry (PIV). The proposed techniques fall in two categories; part 1 of this dissertation considers measurement data processing using constitutive laws and part 2 focuses on development of a coaxial volumetric flow measurement system that uses helium filled soap bubbles (HFSB) as tracer particles.

In part 1, first a technique is proposed to measure instantaneous volumetric pressure using a low repetition rate tomographic PIV system. Instead of time-resolved measurement of the flow temporal evolution, which typically required for pressure-from-PIV procedures, the required temporal information is obtained by solution of the incompressible Navier-Stokes equations in vorticity-velocity formulation using the spatial information available from the instantaneous measurements.

The reverse is proposed for cases where temporal resolution is more abundant, but spatial resolution is limited. The vorticity transport equation is leveraged to couple temporal information with instantaneous velocity data in the proposed VIC+ framework, in an attempt to obtain a dense velocity field at high spatial resolution. The governing principle is that by using the flow governing equations, the data ensemble used for interpolation is increased beyond instantaneous velocity measurements only. The technique is demonstrated to allow for measurement of vorticity and dissipation in a real-world experiment, which would otherwise be underestimated by more than 40% using the established tomographic PIV approach.

The proposed VIC+ technique uses a data ensemble for dense velocity interpolation consisting of the instantaneous velocity and material derivative measurements obtained from Lagrangian particle tracking velocimetry. An extension of the VIC+ framework that uses a measurement time-segment instead of instantaneous data only is shown to potentially improve the measurement fidelity further, when a cost-effective three-dimensional implementation can be realized.

An uncertainty quantification technique is proposed for future developments of such dense interpolation techniques. It is shown that the results from Lagrangian particle tracking measurements can be directly used for uncertainty quantification of dense interpolations and no independent measurement data is required.

In part 2 of this dissertation, a technique is first proposed for large-scale volumetric pressure measurement. The method follows recent developments of large-scale measurements using HFSB tracer particles, in combination with Lagrangian particle tracking and ensemble bin-averaging. This allows for evaluation of accurate velocity statistics and in turn the time-averaged pressure field.

The dissertation concludes with the proposal of the coaxial volumetric velocimeter (CVV). The CVV brings imaging and illumination together in a compact box, viewing and illuminating a measurement volume from a single viewing direction. The theoretical background that is derived shows that measurements in air using the CVV are only possible using tracer particles that scatter significantly more light than traditional micron sized tracer particles. Here, HFSB tracer particles are used. Due to the small solid angle of the imaging system, tracer particles need to be imaged over an extended number of snapshots to increase particle positional accuracy, making use of particle trajectory regularization.

A prototype CVV has been realized, which is first used to confirm that the flow around a sphere is measured with acceptable correspondence to a potential flow solution. Second, in the case of the flow around a cyclist, the CVV is shown to allow for measurements near both concave and convex surfaces within one measurement volume. This allows for flow analysis using skin-friction lines. In addition, the compact nature of the CVV allows mounting on a robotic arm for time-averaged of a large and complex wind tunnel model. The full-scale measurement of the flow around Giro d’Italia cyclist Tom Dumoulin shown using the CVV is an example of the latter.