Assimilation and extension of particle image velocimetry data of turbulent Rayleigh–Bénard convection using direct numerical simulations

A novel method for assimilating and extending measured turbulent Rayleigh–Bénard convection data is presented, which relies on the fractional step method also used to solve the incompressible Navier–Stokes equation in direct numerical simulations. Our approach is used to make measured tomographic particle image velocimetry (tomo PIV) fields divergence-free and to extract temperature fields. Comparing the time average of the extracted temperature fields with the temporally averaged temperature field, measured using particle image thermometry in a subdomain of the flow geometry, shows that extracted fields correlate well with measured fields with a correlation coefficient of $$C_{T\tilde{T}}=0.84$$ C T T ~ = 0.84 . Additionally, extracted temperature fields as well as divergence-free velocity fields serve as initial fields for subsequent direct numerical simulations with and without feedback which generate small-scale turbulence initially absent in the experimental data. Although the tomo PIV data set was spatially under-resolved and did not include any information on the boundary layers, the here-proposed method successfully generates velocity and temperature fields featuring small-scale turbulence and thermal as well as kinetic boundary layers, without disturbing the large-scale circulation contained in the original experimental data significantly. The latter is underpinned by high vertical and horizontal velocity correlation coefficients—computed from velocity fields averaged in time and horizontal x-direction obtained from the measurement and from the simulation without feedback—of $$C_{v\tilde{v}}=0.92$$ C v v ~ = 0.92 and $$C_{w\tilde{w}}=0.91$$ C w w ~ = 0.91 representing the large-scale structure. For simulations with feedback, the generated velocity fields resemble the experimental data increasingly well for higher feedback gain values, whereas the temperature fluctuation intensity deviates noticeably from the values obtained from a direct numerical simulation without feedback for gain values $$\alpha \ge 1$$ α ≥ 1 . Thus, a feedback gain of $$\alpha =0.1$$ α = 0.1 was found optimal with correlation coefficients of $$C_{v\tilde{v}}=0.96$$ C v v ~ = 0.96 and $$C_{w\tilde{w}}=0.95$$ C w w ~ = 0.95 as well as a realistic temperature fluctuation intensity profile. The xt-averaged temperature fields obtained from the direct numerical simulations with and without feedback correlate somewhat less with the extracted temperature field ($$C_{T\tilde{T}}\approx 0.6$$ C T T ~ ≈ 0.6 ), which is presumably caused by spatially under-resolved and temporally oscillating initial tomo PIV fields reflected by the extracted temperature field. Graphical abstract

Forced and mixed convection experiments in a confined vertical backward facing step at low-Prandtl number

In this paper, we present experimental results for a non-isothermal vertical confined backward facing step conducted with a low-Prandtl number fluid. The eutectic alloy gallium–indium–tin is used as the working fluid. We conducted experiments for different Reynolds and Richardson numbers covering both forced and mixed convection regimes. Time-averaged velocity profiles were measured at six streamwise positions along the test section center-plane with so-called permanent magnet probes. The local Nusselt number was measured in streamwise and spanwise directions along the heating plate mounted right after the step. We further ran RANS simulations of the experiment to study the qualitative influence of assuming a constant specific heat flux thermal boundary condition for the experiment heating plate. The measured velocity profiles show the expected behavior for both studied convection regimes, while the measured streamwise local Nusselt number profiles do not. This is explained by how the heating plate thermal boundary condition is defined. We performed an order of magnitude estimate to estimate the forced- to mixed convection transition onset. The estimate shows good agreement with the experimental data, although further measurements are needed to further validate the estimated transition threshold. The measurement of fluctuating quantities remains an open task to be addressed in future experiments, since the permanent magnet probe measurement equation needs further adjustments. Graphical Abstract