Thermal convection of a viscoplastic liquid with high Rayleigh and Bingham numbers (original) (raw)
Related papers
Journal of Non-Newtonian Fluid Mechanics, 2010
A study of heat transport in Rayleigh-Bénard convection in viscoelastic liquids with/without gravity modulation is made using a most minimal representation of Fourier series and a representation with higher modes. The Oldroyd-B constitutive relation is considered. The resulting non-autonomous Lorenz model (generalized Khayat-Lorenz model of four modes and seven modes) is solved numerically using the adaptive-grid Runge-Kutta-Fehlberg45 method to quantify the heat transport. The effect of gravity modulation is shown to be stabilizing there by leading to a situation of reduced heat transfer. The Deborah number is shown to have an antagonistic influence on convection compared to the stabilizing effect of modulation amplitude and elastic ratio. The results in respect of Maxwell, Rivlin-Ericksen and Newtonian liquids are obtained as particular cases of the present study. A transformation of the momentum equations illustrates the equivalence of present approach and the one due to Khayat that uses normal stresses explicitly.
Rayleigh-Bénard convection for viscoplastic fluids
Physics of Fluids, 2013
A study of the static yield stress in a binary Lennard-Jones glass J. Chem. Phys. 120, 2788 (2004 Structural basis for the yield stress in plastic disperse systems Appl. Phys. Lett. 82, 3239 (2003) Electrorheological fluid with an extraordinarily high yield stress
Physics of Fluids, 2023
The effect of viscoelasticity on the flow and heat transport in the Rayleigh-Bénard convection (RBC) in a rectangular with horizontal periodic boundary is investigated via direct numerical simulation. The working fluid is described by the finitely extensible nonlinear elastic-Peterlin (FENE-P) constitutive model that is able to capture some of the most important polymeric flow behaviors. Numerical simulations are conducted at a low concentration β = 0.9, where β = μs/μ0, μs is the solvent viscosity, μ0 = μs + μp is sum of μs and the polymer viscosity μp. A parametric analysis is performed to understand the influence of the Weissenberg number Wi, the viscosity ratio β and the extension length L on the oscillating mode of the viscoelastic RBC. It is found that both Wi and β weakly inhibit the convection onset and the transition from steady to oscillatory convection. The amplitude and frequency of the oscillations in the oscillatory flow regime are both suppressed. However, the elastic nonlinearity may make the flow transition irregular and even may bring about the relaminarization or lead to the convection cells traveling in the horizontal direction. The extension length L may induce multiple pairs of roll flow patterns at a specific setting of (Ra, Wi). Heat transport is reduced by elasticity but still obeys the power law with Ra if the flow pattern has one pair of rolls. However, heat transfer enhancement occurs if multiple pairs of rolls are induced.
Natural Convection of Viscoelastic Liquids
ASME Fluids Engineering Division Summer Meeting, Lake Tahoe, Nevada, USA, Volume: FED-Vol. 179, p. 31-41, 1994
ABSTRACT: Two dimensional natural convection of a nonlinear fluid of the differential type, in an inclined cavity of arbitrary aspect ratio is solved by a regular perturbation for small Grashof numbers. We show that the series are asymptotic in character. Non-Newtonian effects appear at the third order of the analysis even though the Giesekus-Tanner theorem is not valid. The relative contributions of the elastic and shear rate dependent viscosity characteristics of the liquid to the non-Newtonian behavior are investigated through a parametric study, together with the dependence of the Nusselt number on the nonlinear properties of the fluid. The effects of the aspect ratio and the inclination of the enclosure on the flow field and the heat transfer coefficient are also investigated. An interesting instability of the fluid of grade three triggered by elastic effects is discussed together with the implications concerning heat transfer characteristics.
Physical Review Fluids, 2023
The time-dependent oscillating convection leading to the formation of reverse flowing cells is a special phenomenon induced by viscoelasticity in the Rayleigh-Bénard convection (RBC). The causes and the evolution of this overstability problem have not yet been investigated in-depth. Numerical simulations of the viscoelastic Rayleigh-Bénard convection (VRBC) have been conducted in this work with viscoelastic working fluids abiding by the nonlinear Phan-Thien-Tanner (PTT) constitutive structure in two-dimensional cavities. To understand the impact of the nonlinearity and the rheological parameters on the mechanism of the regular reverse flow numerical simulations have been performed over the range of β = (0.1, 0.2) (where β = μs/μ0, μs is the solvent viscosity, μ0 = μs + μp is sum of solvent viscosity μs and polymer viscosity μp) and Weissenberg number (We ∈ [0.075, 0.25]), using an in-house finite-difference code. The remaining constitutive parameters of the (PTT) fluid representing elongational and slippage characteristics of the fluid were kept fixed at = 0.1 and ξ = 0.05, respectively. A viscoelastic kinetic-energy budget method was used to analyze the energy transport in this time-dependent reverse flow process. An original parametric analysis is developed to gain an insight into the dynamics of the reversal flow observed recently in our work, Zheng et al. [Phys. Rev. Fluids 7, 023301 (2022)], as well as observed by Park and Ryu [Rheol. Acta 41, 427 (2002)] and Lappa and Boaro [J. Fluid Mech. 904, A2 (2020)]. The emergence of the reversal convection can be explained by the transfer of potential energy between flow and fluid elasticity during the reversal process. The existence of time phase differences of different potentials in the evolution drive this potential-energy transfers.
Rayleigh–Bénard convection in binary viscoelastic fluid
Physica A: Statistical Mechanics and its Applications, 2000
The onset of convection in a binary-viscoelastic Oldroyd-B uid is investigated. The threshold for oscillatory convection is calculated. It is shown that the critical oscillation frequency may di er by several orders of magnitude on varying separation ratio and Deborah number. The results suggest that binary uid aspects may not be discarded when studying thermal convection in polymeric solutions.
Physics of Fluids, 2023
The oscillating onset of the Rayleigh-Bénard convection (RBC) with viscoelastic fluids in a slightly tilted 2-dimension (2D) rectangular cavity with aspect ratio Γ = 2 was investigated for the first time via direct numerical simulation. A series of simulations were conducted in the plane of the Rayleigh number (Ra) and the tilt angle (α ∈ [0◦,5◦]) with three Weissenberg numbers (Wi = (0.1,0.15,0.2)) at a fixed Prandtl number Pr = 7.0. The evolutionary path of the oscillating convection onset in the (Wi,α)-plane was determined and corresponding complex flow structures were observed. The inclination of the box delays the onset of the oscillations and the corresponding Rayleigh number Rac as compared to the horizontal configuration. Oscillating flow structures acquire the attributes of a traveling wave. A specific feature of the oscillating convection in the case of the horizontal cavity, the periodicity in space and time exists in the inclined box case as well. But, the evolution of the oscillatory flow structure is very different from the horizontal case in that the counter-clockwise cell assimilates the clockwise cell [Physical Review Fluids 7, 023301 (2022)].
Pattern Selection in Rayleigh Bénard Convection with Non-Linear Viscoelastic Fluids
Physical Review Fluids, 2022
Rayleigh-Bénard convection in a rectangular enclosure of aspect ratio 2:1 filled by a class of non-linear viscoelastic fluids represented by the Phan Thien-Tanner (PTT) constitutive equation is investigated numerically. Governing equations are discretized by finite difference methods in space and time. The momentum and PTT constitutive equations are written in a quasi-linear formulation. Quasi-linear terms are treated with the High-Order Upwind Central (HOUC) method and velocity-pressure coupling is handled through the projection method. The developed model is validated for Oldroyd-B type of working fluids. The onset of time-dependent convection is observed and the critical Rayleigh number is determined for PTT type of fluids. Time-dependent flow pattern transition is investigated and explained. Transition from time-dependent flow to steady-state flow is observed at a higher Rayleigh number and the corresponding critical Rayleigh number is computed, for the first time in the literature. This is a new original finding. The effect of the rheological parameters on heat transfer is investigated.
A New Approach to the Numerical Modeling of the Viscoelastic Rayleigh-Bénard Convection
Conference: ASME 2019 International Mechanical Engineering Congress and Exposition, Salt Lake City, Utah USA November 11-14, 2019; IMECE 2019 Proceedings, Paper No. IMECE2019-11675; published online January 21, 2020, ASME Digital Collection, 2019
A new approach to the numerical simulation of incompressible viscoelastic Rayleigh-Bénard convection in a cavity is presented. Due to the fact that the governing equations are of elliptic-hyperbolic type, a quasi-linear treatment of the hyperbolic part of the equations is proposed to overcome the strong instabilities that can be induced and is handled explicitly in time. The elliptic part related to the mass conservation and the diffusion is treated implicitly in time. The time scheme used is semi-implicit and of second order. Second-order central differencing is used throughout except for the quasi-linear part treated by third order space scheme HOUC. Incompressibility is handled by a projection method. The numerical approach is validated first through comparison with a Newtonian benchmark of Rayleigh-Bénard convection and then by comparing the results related to the convection setup in a 2 : 1 cavity filled with an Oldroyd-B fluid. A preliminary study is also conducted for a PTT fluid and shows that PTT fluid is slightly more unstable than Oldroyd-B fluid in the configuration of Rayleigh-Bénard convection.