Numerical instability investigation of inward radial Rayleigh–Bénard–Poiseuille flow

2021 ◽  
Vol 33 (3) ◽  
pp. 034120
Author(s):  
M. K. Hasan ◽  
A. Gross
Keyword(s):  
Poiseuille Flow ◽  
Numerical Instability ◽  
Rayleigh Benard

Convective and absolute instabilities in Rayleigh–Bénard–Poiseuille mixed convection for viscoelastic fluids

2015 ◽  
Vol 765 ◽  
pp. 167-210 ◽  
Author(s):  
S. C. Hirata ◽  
L. S. de B. Alves ◽  
N. Delenda ◽  
M. N. Ouarzazi
Keyword(s):  
Rayleigh Number ◽  
Mixed Convection ◽  
Poiseuille Flow ◽  
Flow Direction ◽  
Viscoelastic Fluids ◽  
Newtonian Fluids ◽  
Absolute Instability ◽  
Elastic Regime ◽  
Elasticity Number ◽  
Rayleigh Benard

AbstractThe convective and absolute nature of instabilities in Rayleigh–Bénard–Poiseuille (RBP) mixed convection for viscoelastic fluids is examined numerically with a shooting method as well as analytically with a one-mode Galerkin expansion. The viscoelastic fluid is modelled by means of a general constitutive equation that encompasses the Maxwell model and the Oldroyd-B model. In comparison to Newtonian fluids, two more dimensionless parameters are introduced, namely the elasticity number${\it\lambda}_{1}$and the ratio${\it\Gamma}$between retardation and relaxation times. Temporal stability analysis of the basic state showed that the three-dimensional thermoconvective problem can be Squire-transformed. Therefore, one must distinguish mainly between two principal roll orientations: transverse rolls TRs (rolls with axes perpendicular to the Poiseuille flow direction) and longitudinal rolls LRs (rolls with axes parallel to the Poiseuille flow direction). The critical Rayleigh number for the appearance of LRs is found to be independent of the Reynolds number ($\mathit{Re}$). Depending on${\it\lambda}_{1}$and${\it\Gamma}$, two different regimes can be distinguished. In the weakly elastic regime, the emerging LRs are stationary, while they are oscillatory in the strongly elastic regime. For TRs, it is found that in the weakly elastic regime, the stabilization effect of$\mathit{Re}$is more important than in Newtonian fluids. Moreover, for sufficiently elastic fluids a jump is observed in the oscillation frequencies and wavenumbers for moderate$\mathit{Re}$. In the strongly elastic regime, the effect of the imposed throughflow is to promote the appearance of the upstream moving TRs for low values of$\mathit{Re}$, which are replaced by downstream moving TRs for higher values of $\mathit{Re}$. Moreover, the results proved that, contrary to the case where$\mathit{Re}=0$, the elasticity number${\it\lambda}_{1}$(the ratio${\it\Gamma}$) has a strongly stabilizing (destabilizing) effect when the throughflow is added. The influence of the rheological parameters on the transition curves from convective to absolute instability in the Reynolds–Rayleigh number plane is also determined. We show that the viscoelastic character of the fluid hastens the transition to absolute instability and even may suppress the convective/absolute transition. Throughout this paper, similarities and differences with the corresponding problem for Newtonian fluids are highlighted.

STABILITY OF A RAYLEIGH-BENARD POISEUILLE FLOW CONSIDERING A CARREAU FLUID

2018 ◽  
Author(s):  
Vítor José Jerônimo de Moraes ◽  
Pedro Vayssiere Brandão ◽  
Leonardo Santos de Brito Alves
Keyword(s):  
Poiseuille Flow ◽  
Carreau Fluid ◽  
Rayleigh Benard

scholarly journals Experimental investigation into localized instabilities of mixed Rayleigh–Bénard–Poiseuille convection

2009 ◽  
Vol 640 ◽  
pp. 401-419 ◽  
Author(s):  
EMERIC GRANDJEAN ◽  
PETER A. MONKEWITZ
Keyword(s):  
Poiseuille Flow ◽  
Flow Direction ◽  
Vertical Channel ◽  
System Response ◽  
Channel Height ◽  
Nonlinear Modes ◽  
Prandtl Numbers ◽  
The Stability ◽  
The One ◽  
Rayleigh Benard

The stability of the Rayleigh–Bénard–Poiseuille flow in a channel with large transverse aspect ratio (ratio of width to vertical channel height) is studied experimentally. The onset of thermal convection in the form of ‘transverse rolls’ (rolls with axes perpendicular to the Poiseuille flow direction) is determined in the Reynolds–Rayleigh number plane for two different working fluids: water and mineral oil with Prandtl numbers of approximately 6.5 and 450, respectively. By analysing experimental realizations of the system impulse response it is demonstrated that the observed onset of transverse rolls corresponds to their transition from convective to absolute instability. Finally, the system response to localized patches of supercriticality (in practice local ‘hot spots’) is observed and compared with analytical and numerical results of Martinand, Carrière & Monkewitz (J. Fluid Mech., vol. 502, 2004, p. 175 and vol. 551, 2006, p. 275). The experimentally observed two-dimensional saturated global modes associated with these patches appear to be of the ‘steep’ variety, analogous to the one-dimensional steep nonlinear modes of Pier, Huerre & Chomaz (Physica D, vol. 148, 2001, p. 49).

Nonlinear stability of the Bingham Rayleigh–Bénard Poiseuille flow

2009 ◽  
Vol 158 (1-3) ◽  
pp. 127-131 ◽  
Author(s):  
Christel Métivier ◽  
Ian A. Frigaard ◽  
Chérif Nouar
Keyword(s):  
Nonlinear Stability ◽  
Poiseuille Flow ◽  
Rayleigh Benard
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