Extraction of temperature fields from PIV data of turbulent Rayleigh-Bénard convection using DNS

Abstract

To gain insights into the dynamical processes that govern the problem of turbulent Rayleigh-Bénard convection, information about the temperature field---next to the velocity field---is required. In the present study, we exploit the governing flow equations to extract the temperature field from a velocity field measured via tomographic particle image velocimetry. The methods used within this study are derived from algorithms originally used in the framework of direct numerical simulations. First, we enforce the divergence-free condition on the measured velocity field using a fractional-step method based on a Poisson equation. Second, we extract the temperature field from the velocity field via the momentum equation. Third, we extract the temperature field from the velocity field via the solution of the stationary convection-diffusion equation. The extracted velocity field---together with the corresponding divergence-free velocity field---can serve as an initial condition for a direct numerical simulation of the problem. Validating the extraction method based on the stationary convection-diffusion equation with data from direct numerical simulations shows a good correlation coefficient between the extracted and the simulated temperature field (0.86). Although the third method incorporates the ambitious assumption of stationarity, temperature fields are successfully extracted from the measured velocity fields. However, with a correlation coefficient of 0.57, the agreement between the average extracted temperature field and the average temperature field measured in a subvolume of the flow domain is somewhat less than the one found in the simulated data. The latter is presumably attributed not only to the extraction method, but also to the underlying measurement data. Thus, an increase in measurement accuracy in future applications is likely to improve the accuracy of the extraction methods as well.