Stability of Poiseuille flow in an anisotropic porous layer with oblique principal axes: More accurate solution

2022

J. Fluid Mech.

Self Cite

The linear stability of thermal buoyant flow in a fluid-saturated vertical porous slab is studied under the assumption of weak and strong horizontal heterogeneities of the permeability. The two end vertical isothermal boundaries are impermeable and some paradigmatic cases of linear, quadratic and exponential heterogeneity models are deliberated. The stability/instability of the basic flow is examined by carrying out a numerical solution of the governing equations for the disturbances as Gill's proof (A.E. Gill, J. Fluid Mech, vol. 35, 1969, pp. 545–547) of linear stability is found to be ineffective. The possibilities of base flow becoming unstable due to heterogeneity in permeability are recognized, in contrast to Gill's stability problem. The neutral stability curves are presented and the critical Darcy–Rayleigh number for the onset of convective instability is computed for different values of the variable permeability constant. The similarities and differences between different heterogeneity models on the stability of fluid flow are clearly discerned.

Section: Numerical Proceduresmentioning

confidence: 99%

Gill's stability problem may be unstable with horizontal heterogeneity in permeability

2022

J. Fluid Mech.

Self Cite

“…Repeating this procedure for different values of , the marginal stability curve is obtained, say and the corresponding frequency . The critical values and are then obtained for specified values of and 30 , 31 . If then the critical disturbance modes are stationary otherwise they are travelling-waves.…”

Section: Numerical Proceduresmentioning

confidence: 99%

“…) and c c (a c , R S , H, γ , α, Le) are then obtained for specified values of R S , H, γ , α and Le30,31 . If c c = 0 then the critical disturbance modes are stationary otherwise they are travelling-waves.…”

mentioning

confidence: 99%

The role of a second diffusing component on the Gill–Rees stability problem

Nagamani

2022

Sci Rep

The stability of natural convection in a vertical porous layer using a local thermal nonequilibrium model was first studied by Rees (Transp Porous Med 87:459–464, 2011) following the proof of Gill (J Fluid Mech 35:545–547, 1969), called the Gill–Rees stability problem. The aim of the present study is to investigate the implication of an additional solute concentration field on the Gill–Rees problem. The stability eigenvalue problem is solved numerically and some novel results not observed in the studies of double-diffusive natural convection in vertical porous (local thermal equilibrium case) and non-porous layers are disclosed. The possibility of natural convection parallel flow in the basic state becoming unstable due to the addition of an extra diffusing component is established. In some cases, the neutral stability curves of stationary and travelling-wave modes are connected to form a loop within which the flow is unstable indicating the requirement of two thermal Darcy–Rayleigh numbers to specify the stability/instability criteria. Moreover, the change in the mode of instability is recognized in some parametric space. The results for the extreme cases of the scaled interphase heat transfer coefficient are discussed.

“…The above generalized eigenvalue problem usually describes the linear stability boundary of the basic flow, and the eigenvalues of the eigenvalue problem are calculated by using QZ algorithm (Moler and Stewart 26 ). A suitable environment for the implementation of these steps is carried out using Mathematica 11.3 software (for a detailed procedure, see Shankar et al 27 – 29 ).…”

Section: Computation Of the Eigenvaluementioning

confidence: 99%

Benchmark solution for the stability of plane Couette flow with net throughflow

2021

Sci Rep

This paper investigates the stability of an incompressible viscous fluid flow between relatively moving horizontal parallel plates in the presence of a uniform vertical throughflow. A linear stability analysis has been performed by employing the method of normal modes and the resulting stability equation is solved numerically using the Chebyshev collocation method. Contrary to the stability of plane Couette flow (PCF) to small disturbances for all values of the Reynolds number in the absence of vertical throughflow, it is found that PCF becomes unstable owing to the change in the sign of growth rate depending on the magnitude of throughflow. The critical Reynolds number triggering the instability is computed for different values of throughflow dependent Reynolds number and it is shown that throughflow instills both stabilizing and destabilizing effect on the base flow. It is seen that the direction of throughflow has no influence on the stability of fluid flow. A comparative study between plane Poiseuille flow and PCF has also been carried out and the similarities and differences are highlighted.