arXiv subjects

Tapan Kumar Hota

Publications and source records attributed to Tapan Kumar Hota.

4 recordsLinked to original sources

arXiv2018

Nonmodal stability analysis of miscible viscous fingering with non-monotonic viscosity profiles

A non-modal linear stability analysis (NMA) of the miscible viscous fingering in a porous medium is studied for a toy model of non-monotonic viscosity variation. The onset of instability and its physical mechanism are captured in terms of the singular values of the propagator matrix corresponding to the non-autonomous linear equations. We discuss two types of non-monotonic viscosity profiles, namely, with unfavorable (when a less viscous fluid displaces a high viscous fluid) and with favorable (when a more viscous fluid displaces a less viscous fluid) end-point viscosities. A linear stability analysis yields instabilities for such viscosity variations. In addition, we also show that to understand the spatiotemporal evolution of the perturbations it is necessary to analyse the viscosity gradient with respect to the concentration and the location of the maximum concentration $c_m$. For the favorable end-point viscosities, a weak transient instability is observed when the viscosity maximum moves close to the pure invading or defending fluid. This instability is attributed to an interplay between the sharp viscosity gradient and the favorable end-point viscosity contrast. We demonstrate the dissimilarity between the quasi-steady-state approach and NMA in finding the correct perturbation structure and the onset, for both the favorable and unfavorable viscosity profiles. The correctness of the linear perturbation structure obtained from the non-modal stability analysis is validated through nonlinear simulations. We have found that the nonlinear simulations and NMA results are in good agreement. In summary, a non-monotonic variation of the viscosity of a miscible fluid pair is seen to have a larger influence on the onset of fingering instabilities, than the corresponding Arrhenius type relationship.

physics.flu-dyn↗

arXiv2015

Non-modal linear stability analysis of miscible viscous fingering in porous media

The non-modal linear stability of miscible viscous fingering in a two dimensional homogeneous porous medium has been investigated. The linearized perturbed equations for Darcy's law coupled with a convection-diffusion equation is discretized using finite difference method. The resultant initial value problem is solved by fourth order Runge-Kutta method, followed by a singular value decomposition of the propagator matrix. Particular attention is given to the transient behavior rather than the long-time behavior of eigenmodes predicted by the traditional modal analysis. The transient behaviors of the response to external excitations and the response to initial conditions are studied by examining the $ε-$pseudospectra structures and the largest energy growth function. With the help of non-modal stability analysis we demonstrate that at early times the displacement flow is dominated by diffusion and the perturbations decay. At later times, when convection dominates diffusion, perturbations grow. Furthermore, we show that the dominant perturbation that experiences the maximum amplification within the linear regime lead to the transient growth. These two important features were previously unattainable in the existing linear stability methods for miscible viscous fingering. To explore the relevance of the optimal perturbation obtained from non-modal analysis, we performed direct numerical simulations using a highly accurate pseudo-spectral method. Further, a comparison of the present stability analysis with existing modal and initial value approach is also presented. It is shown that the non-modal stability results are in better agreement, than the other existing stability analyses, with those obtained from direct numerical simulations.

physics.flu-dyn↗

arXiv2015

Influence of viscosity contrast on buoyantly unstable miscible fluids in porous media

The influence of viscosity contrast on buoyantly unstable miscible fluids in a porous medium is investigated through a linear stability analysis (LSA) as well as direct numerical simulations (DNS). The linear stability method implemented in this paper is based on an initial value approach, which helps to capture the onset of instability more accurately than the quasi-steady state analysis. In the absence of displacement, we show that viscosity contrast delays the onset of instability in buoyantly unstable miscible fluids. Further, it is observed that suitably choosing the viscosity contrast and injection velocity a gravitationally unstable miscible interface can be stabilized completely. Through LSA we draw a phase diagram, which shows three distinct stability regions in a parameter space spanned by the displacement velocity and the viscosity contrast. DNS are performed corresponding to parameters from each regime and the results obtained are in accordance with the linear stability results. Moreover, the conversion from a dimensionless formulation to the other and its essence to compare between two different type of flow problems associated with each dimensionless formulation are discussed.

physics.flu-dyn↗

arXiv2015

Onset of fingering instability in a finite slice of adsorbed solute

The effect of a linear adsorption isotherm on the onset of fingering instability in a miscible displacement in the application of liquid chromatography, pollutant contamination in aquifers etc. is investigated. Such fingering instability on the solute dynamics arise due to the miscible viscus fingering (VF) between the displacing fluid and sample solvent. We use a Fourier pseudo-spectral method to solve the initial value problem appeared in the linear stability analysis. The present linear stability analysis is of generic type and it captures the early time diffusion dominated region which was never expressible through the quasi-steady state analysis (QSSA). In addition, it measures the onset of instability more accurately than the QSSA methods. It is shown that the onset time depends non-monotonically on the retention parameter of the solute adsorption. This qualitative influence of the retention parameter on the onset of instability resemblances with the results obtained from direct numerical simulations of the nonlinear equations. Moreover, the present linear stability method helps for an appropriate characterisation of the linear and the nonlinear regimes of miscible VF instability and also can be useful for the fluid flow problems with the unsteady base-state.

physics.flu-dyn↗