Effects of Rayleigh-Benard convection on spectra of viscoplastic fluids

摘要

Direct Numerical Simulations (DNS) have been conducted to analyse velocity and temperature spectra in unsteady three-dimensional Rayleigh-Benard convection (differentially heated horizontal walls, i.e. heated from below and cooled from above whereas the other walls are adiabatic) at high nominal Rayleigh number of viscoplastic fluids obeying a Bingham model in cubic domains and the corresponding Newtonian cases with same nominal Rayleigh and Prandtl numbers for reference purposes. The simulations have been carried out for nominal Rayleigh numbers of 10~7 and 10~8 for a representative value of nominal Prandtl number (i.e. Pr = 320 which corresponds to a 0.05% by weight Carbopol-water solution). The effects of yield stress on velocity and temperature spectra and heat transfer characteristics of the flow fields have been investigated in terms of isotherms, path lines, apparently unyielded regions and mean Nusselt number, along with the power spectral densities of temperature and velocity fluctuations. It has been found that thermal convection strengthens (weakens) with increasing nominal Rayleigh number Ra (Bingham number Bn). Consistent with this observation, the range of flow structures becomes larger with higher (smaller) values of Ra (Bn). Additionally, it has been observed that the decay of the power spectral densities of temperature fluctuations in the viscous-convective range is close to the inverse of frequency f(i.e. it scales as f~(-1)) for Pr > 1 in both Newtonian (i.e. Bn = 0) and Bingham fluid cases with moderate values of Bn. The fluid motion (including its unsteady features) weakens and the mean Nusselt number drops progressively with an increase in Bingham number.