Measuring the four fields in high-speed aerodynamics: Pressure, temperature and density from velocity using the Matrix Omnidirectional Pressure Integrator

With the introduction of full-field, 3D velocity measurement techniques and the recent developments in rapid and accurate solution of pressure from PIV in large 3D domains, it is now possible to obtain measurements of the remaining thermodynamic variables (temperature and density) exclusively from field velocity (PIV, PTV) measurements in complex domains, enabling the reconstruction of volumetric measurements that can usher new physical understanding of the topologies of complex, practical flows under highly compressible conditions. The development of the one-shot matrix-based omnidirectional pressure integrator (OS-MODI, Zigunov & Charonko, 2024) enables the reconstruction of large 3D domains with cropped boundaries in a few seconds on a consumer-grade graphics card, requiring no specification of boundary conditions except for a reference pressure at a node on the free stream. This opens new doors for reconstruction of all four field variables in a compressible fluid flow exclusively from PIV measurements.

In this work, a detailed discussion will be presented on the steps required to obtain such measurements in complex flow fields with a tomographic or a scanning stereoscopic PIV system, the trade-offs and limitations involved, the data processing techniques used and examples of applications to complex fluid flows generated in a lab, such as wind tunnel flows at subsonic and supersonic conditions and high-speed jets. Further discussion on the current limitations and next development steps will be presented.