Using a statistical approach based on the unsteady Reynolds-averaged Navier-Stokes equations (URANS) and ensemble averaging, pressure evaluation of spray-induced flow is conducted by means of stereo-particle image velocimetry. The method allows the determination of the full velocity gradient tensor in order to characterize the governing equations. The spray-induced flow of a two-hole gasoline direct injection (GDI) research sample is investigated at 100 bar injection pressure, 1 bar ambient gas pressure, 25 °C fuel and ambient gas temperature. Low-and high-pressure regions are observed representing entrainment, displacement and recirculation flow. In reference to the ambient pressure, the mean pressure field indicates small pressure differences in the order of 0.1 mbar. For the assessment of pressure evaluation, a comparative measurement with a pressure sensor is carried out, which shows good agreement of the temporal pressure course in the intermediate spray region. The propagation of instantaneous velocity uncertainties to the pressure field indicates low pressure uncertainties for an ensemble average of 50 measurement samples. As a result of scale analysis, the pressure gradient is mainly described by the local acceleration, whereas the contribution of convective acceleration and Reynolds stresses focuses in the spray proximity. The analysis shows negligible effects of viscosity and gravity. The sprayinduced flow is regarded as incompressible in case of low mass and heat transfer. The observations justify a simplification of the governing equations minimizing measurement and computational expense.
A novel approach, which utilizes astigmatism-based depth codification and discrete dual-plane illumination, is developed to provide information on the full velocity-gradient tensor in pair of planar domains by means of stereoscopic particle image velocimetry (stereo-PIV). The technique is accordingly referred to as dual-plane stereo-astigmatism (DPSA). In contrast to conventional stereo-PIV, DPSA provides the determination of the desired out-of-plane gradient. The principle of the DPSA approach relies on the joint recording of two, consecutive, planar measurement domains and the subsequent allocation of particles based on their particle image shapes. For the identification of particles, a correlation-based particle identification approach (CPI), which addresses non-overlapping particles, is introduced. With regard to dense particle fields, a method for the iterative particle reconstruction (IPR) is adapted for DPSA. For displacement analysis, a modified PIV evaluation strategy is introduced, which utilizes derived information of particle locations. The DPSA approach is tested experimentally and synthetically by applying it to spray-induced flow measurement and synthetic images generated from DNS data of a turbulent boundary flow. Separate planar velocity fields are obtained by means of PIV and PTV evaluation. A performance analysis is carried out to assess the influence of noise, particle density and particle image size on the procedure of particle identification and allocation. The CPI technique provides adequate results for low to medium particle densities and further features a high robustness regarding particle identification with respect to background noise, optical aberrations and non-uniform particle images. The adapted IPR method, on the other hand, shows viable results for particle densities of up to 0.1 ppp.
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