Ultra-high-speed tomographic digital holographic velocimetry in supersonic particle-laden jet flows

Ultra-high-speed tomographic digital holographic velocimetry is used to measure the three-component, three-dimensional velocities and trajectories of micron-sized particles in a supersonic underexpanded jet flow. In high-speed digital in-line holography, the depth resolution or depth of field is severely restricted by the limited resolution of the digital recording array, which leads to significant elongation of the reconstructed particles in the depth direction. It is shown that by applying tomographic digital holography, this limitation imposed by the high-speed recording array is relaxed and that the accurate reconstruction of 3D particle intensities is possible without the depth-of-field problem. This method is demonstrated by measuring 110 μm solid particles suspended in a 'mildly underexpanded' jet with a nozzle pressure ratio of 2.0. The interference pattern produced by both the suspended particles and the density gradient field is simultaneously recorded by two digital high-speed cameras at a frame rate of 500 000 fps with an exposure time of 250 ns. Individual object fields are reconstructed by tomographic holography and the velocity of the micron-sized particles is analyzed by cross-correlation particle tracking velocimetry. The accuracy of the particle velocity measurements is estimated to be within 5 m s−1 or approximately 4.5% of the particle velocity. In addition, the method is used to study the particle-flow interactions by means of coherent imaging, which reveals a complex interaction between the micron-sized particles and the flow structure of this high-speed 3D unsteady turbulent particle-laden flow.