Numerical Investigation of Hydrodynamic Stability of Inward Radial Rayleigh-Bènard-Poiseuille Flow

2018 ◽  
Author(s):  
Md Kamrul Hasan ◽  
Andreas Gross
Keyword(s):  
Numerical Investigation ◽  
Hydrodynamic Stability ◽  
Poiseuille Flow ◽  
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.

Hydrodynamic stability in plane Poiseuille flow with finite amplitude disturbances

1972 ◽  
Vol 51 (4) ◽  
pp. 687-704 ◽  
Author(s):  
W. D. George ◽  
J. D. Hellums
Keyword(s):  
Reynolds Number ◽  
Linear Theory ◽  
Hydrodynamic Stability ◽  
Poiseuille Flow ◽  
Classical Problem ◽  
Finite Amplitude ◽  
Navier Stokes ◽  
Plane Poiseuille Flow ◽  
Navier Stokes Equation ◽  
Numerical Process

A general method for studying two-dimensional problems in hydrodynamic stability is presented and applied to the classical problem of predicting instability in plane Poiseuille flow. The disturbance stream function is expanded in a Fourier series in the axial space dimension which, on substitution into the Navier-Stokes equation, leads to a system of parabolic partial differential equations in the coefficient functions. An efficient, stable and accurate numerical method is presented for solving these equations. It is demonstrated that the numerical process is capable of accurate reproduction of known results from the linear theory of hydrodynamic stability.Disturbances that are stable according to linear theory are shown to become unstable with the addition of finite amplitude effects. This seems to be the first work of quantitative value for disturbances of moderate and larger amplitudes. A relationship between critical amplitude and Reynolds number is reported, the form of which indicates the existence of an absolute critical Reynolds number below which an arbitrary disturbance cannot be made unstable, no matter how large its initial amplitude. The critical curve shows significantly less effect of amplitude than do those obtained by earlier workers.

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
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