Effects of Prandtl number in two-dimensional turbulent convection

We report a numerical study of the Prandtl-number(Pr)effects in two-dimensional turbulent Rayleigh-Bénard convection.The simulations were conducted in a square box over the Pr range from 0.25 to 100 and over the Rayleigh number(Ra)range from 10^(7) to 10^(10).We find that both the strength and the stability of the large-scale flow decrease with the increasing of Pr,and the flow pattern becomes plume-dominated at high Pr.The evolution in flow pattern is quantified by the Reynolds number(Re),with the Ra and the Pr scaling exponents varying from 0.54 to 0.67 and-0.87 to-0.93,respectively.It is further found that the non-dimensional heat flux at small Ra diverges strongly for different Pr,but their difference becomes marginal as Ra increases.For the thermal boundary layer,the spatially averaged thicknesses for all the Pr numbers can be described byδθ~Ra^(-0.30) approximately,but the local values vary a lot for different Pr,which become more uniform with Pr increasing.

Characteristics of temperature fluctuation in two-dimensional turbulent Rayleigh-Bénard convection

We study the characteristics of temperature fluctuation in two-dimensional turbulent Rayleigh–Benard convection in´a square cavity by direct numerical simulations.The Rayleigh number range is 1×10^(8)≤Ra≤1×10^(13),and the Prandtl number is selected as Pr=0.7 and Pr=4.3.It is found that the temperature fluctuation profiles with respect to Ra exhibit two different distribution patterns.In the thermal boundary layer,the normalized fluctuationθrms/θrms,max is independent of Ra and a power law relation is identified,i.e.,θrms/θrms,max∼(z/δ)0.99±0.01,where z/δis a dimensionless distance to the boundary(δis the thickness of thermal boundary layer).Out of the boundary layer,when Ra≤5×10^(9),the profiles ofθrms/θrms,max descend,then ascend,and finally drop dramatically as z/δincreases.While for Ra≥1×10^(10),the profiles continuously decrease and finally overlap with each other.The two different characteristics of temperature fluctuations are closely related to the formation of stable large-scale circulations and corner rolls.Besides,there is a critical value of Ra indicating the transition,beyond which the fluctuation hθrmsiV has a power law dependence on Ra,given by hθrmsiV∼Ra−0.14±0.01.

Gaussian process regressions on hot deformation behaviors of FGH98 nickel-based powder superalloy

The hot deformation behaviors of FGH98 nickel-based powder superalloy were experimentally investigated and theoretically analyzed by Arrhenius models and machine learning(ML).Hot compression tests were conducted with a Gleeble-3800 thermo-mechanical simulation machine on the FGH98 superalloy at strain rates of 0.001–1 s–1 and temperatures of 1025–1175℃.The peak stresses under different deformation conditions were analyzed via the Sellars model and an ML-inspired Gaussian process regression(GPR)model.The prediction of the GPR model outperformed that from the Sellars model.In addition,the stress-strain responses were predicted by the GPR model and tested by experimentally measured stress-strain curves.The results indicate that the developed GPR model has great power with wide generalization capability in the prediction of hot deformation behaviors of FGH98 superalloy,as evidenced by the R2 value higher than 0.99 on the test dataset.