Benzi Roberto, Ching Emily S C, De Angelis Elisabetta
Dipartimento di Fisica, Università di Roma Tor Vergata and INFN, via della Ricerca Scientifica 1, 00133 Roma, Italy.
Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong.
Phys Rev E. 2016 Dec;94(6-1):063110. doi: 10.1103/PhysRevE.94.063110. Epub 2016 Dec 21.
We study how polymers affect the heat flux in turbulent Rayleigh-Bénard convection at moderate Rayleigh numbers using direct numerical simulations with polymers of different relaxation times. We find that heat flux is enhanced by polymers and the amount of heat enhancement first increases and then decreases with the Weissenberg number, which is the ratio of the polymer relaxation time to the typical time scale of the flow. We show that this nonmonotonic behavior of the heat flux enhancement is the combined effect of the decrease in the viscous energy dissipation rate due to the viscosity of the Newtonian fluid and the increase in the energy dissipation rate due to polymers when Weissenberg number is increased. We explain why the viscous energy dissipation rate decreases with the Weissenberg number. Then by carrying out a generalized boundary layer analysis supplemented by a space-dependent effective viscosity from the numerical simulations, we provide a theoretical understanding of the change of the heat flux when the viscous energy dissipation rate is held constant. Our analysis thus provides a physical way to understand the numerical results.
我们使用具有不同松弛时间的聚合物进行直接数值模拟，研究了在中等瑞利数下聚合物如何影响湍流瑞利 - 贝纳德对流中的热通量。我们发现聚合物会增强热通量，并且热增强量首先随着魏森贝格数增加，然后随着魏森贝格数减小，魏森贝格数是聚合物松弛时间与流动典型时间尺度的比值。我们表明，热通量增强的这种非单调行为是由于牛顿流体粘度导致的粘性能量耗散率降低与魏森贝格数增加时聚合物导致的能量耗散率增加的综合效应。我们解释了为什么粘性能量耗散率会随着魏森贝格数降低。然后，通过进行广义边界层分析，并结合数值模拟中与空间相关的有效粘度，当粘性能量耗散率保持恒定时，我们对热通量的变化提供了理论理解。因此，我们的分析提供了一种理解数值结果的物理方法。
