Girish Kumar Rajan

The flow of a Newtonian fluid through long, slender, axisymmetric tubes with spatially varying diameters is investigated in this study. Employing a higher order asymptotic analysis, the velocity and pressure fields are systematically derived for steady, incompressible flow through an arbitrary shaped tube, with the analysis restricted to cases in which the physical Reynolds number is less than unity. Numerical simulations are performed to validate the asymptotic solutions and ensure their accuracy. Based on the asymptotic analysis, tube geometries are classified into two categories: unconditioned tubes, where the wall surface is not sufficiently flat at the ends, and conditioned tubes, where the wall surface is sufficiently flat at both inlet and outlet. Deviations between asymptotic and numerical results arise at the tube inlet for unconditioned geometries due to mismatched boundary conditions stemming from the absence of conditioning. These deviations are shown to vanish when a non-parabolic velocity profile is imposed as the inlet condition in numerical simulations. Additionally, it is shown that asymptotic solutions remain valid over broader parameter ranges for flows within unconditioned tubes, while their applicability is more restricted for flows within conditioned tubes. These results are extended to the case of fluid transport through periodically constricted wavy-walled tubes, commonly encountered in biological systems. Finally, numerical results for a specific tube geometry are compared with experimental data on incipient laminar flow separation, offering further insight into flow behavior under adverse pressure gradients in constricted geometries.

Enhancing the dissipation of fluid energy generated due to sloshing is necessary to eliminate the undesirable hydrodynamic forces it produces on the walls of a mobile container. With this goal, this work investigates the fluid motion due to sloshing in three rectangular tanks (A, B, and C) that undergo sinusoidal displacements from their mean positions for a short duration of time, Ts. Tank A is partially filled with water; tank B is partially filled with water and contains a bottom-mounted baffle at a distance of xb from the left wall; and tank C consists of an oil-layer of thickness, d, floating on a water layer. Three-dimensional simulations are performed to obtain the flow field and temporal evolution of fluid kinetic energy in several cases. The period of evolution includes the initial transient regime; the periodic forced-oscillation regime; and the free-oscillation regime, which comprises the nonlinear and linear damping sub-regimes. In each case, nonlinear and linear damping rates are obtained and analyzed to estimate the timescales for energy dissipation in the respective sub-regimes. Results of detailed parametric studies reveal that damping rates increase significantly due to the baffle (tank B) and oil-layer (tank C), so both are effective in mitigating sloshing. For flow in tank B, nonlinear damping rates are consistently higher than corresponding linear damping rates, and both are non-monotonic functions of xb and Ts. For flow in tank C, the nonlinear (linear) damping rate is a monotonic (non-monotonic) function of d. Reasons for variations in damping rates due to the baffle and the oil-layer are highlighted, and discussions of the physics causing these changes are also presented.

The air-sea interface is in general contaminated due to the presence of surfactants, such as those resulting from oil spills. Recently, a three-fluid model was developed for the dissipation of capillary-gravity waves, wherein the interfacial fluid was allowed to be a Newtonian layer of finite thickness. Realizing that oil spills can result in the formation of emulsions on the water surface, we perform simple experiments to investigate the rheology of such emulsions. In this preliminary report of our ongoing work, we present results which reveal that interfacial fluid films composed of such emulsions are likely to be non-Newtonian. Our aim is to generalize the three-fluid Newtonian model, by accounting for the complex rheology of interfacial fluid films. We plan to use appropriate rheological models for such non-Newtonian interfacial films in our future analyses on wave dissipation to obtain more accurate results.

We investigate the dissipation of linear, two-dimensional, interfacial waves in a setting comprising three fluids (an upper fluid of semi-infinite depth, a middle fluid-layer of finite thickness, and a lower fluid of semi-infinite depth) separated by two distinct interfaces, which we consider to be elastic. We derive analytic expressions for the dissipation rate of capillary-gravity waves in such a system, in both the barotropic and baroclinic modes of propagation. Using the dissipation rate model formulated herein, we conduct parametric studies of barotropic gravity waves in an air–oil–water system. We consider six different wavenumbers within the range of 0.0165 m⁻¹ (corresponding to ocean swell) to 44.5 m⁻¹ (corresponding to a typical laboratory gravity wave) and investigate the effects of three major mechanisms of loss of energy, which are the dissipation due to the (i) dynamics in the upper fluid (air), (ii) elastic interfaces, and (iii) viscous middle fluid (oil) layer of finite thickness. For waves with wavenumbers of 0.0165 m⁻¹ and 0.04 m⁻¹, the dominant mechanism for the energy loss is that due to the dynamics in air. For waves with wavenumbers of 1 m⁻¹ and 4 m⁻¹, the oil layer acts to increase the dissipation rates significantly but only when its thickness is beyond a threshold value. For waves with wavenumbers of 36.2 m⁻¹ and 44.5 m⁻¹, the elastic interfaces cause significant increases in the dissipation rates, when their elasticities change from a value of 0.01 N/m to 0.0225 N/m. The three-fluid model developed herein is applicable to capillary-gravity waves propagating in a generic fluid system with arbitrary values for the densities, viscosities, interfacial elasticities, and with an arbitrary value for the middle fluid-layer thickness within an upper limit. This model is useful in predicting the dissipation rates of waves on the ocean surface, which is (in general) covered with biofilms and oil layers of thicknesses ranging from a few μm to a few mm, and in predicting the dissipation rates of waves such as swell, for which the dynamics in the upper fluid (air) are important.

Two-dimensional linear waves at a contaminated interface separating two infinitely deep fluids of arbitrary densities and viscosities are investigated. The contamination is modeled as a massless monolayer, which may result from insoluble surfactants, and introduces interfacial elasticity. Thus, the interface supports two wave modes: transverse, capillary-gravity waves (CG-waves) and longitudinal, Marangoni waves (M-waves). A comprehensive dispersion relation is derived; it can be solved numerically to obtain the complex-valued frequency as a function of the irrotational wavenumber for the CG-waves and for the M-waves. The CG-waves are analyzed in this paper; the M-waves are analyzed in a separate work. The main result here is the derivation of an operational approximate formula for the temporal decay rate of the CG-waves. Its predictions are compared to the available measurements of (laboratory) gravity waves, ocean swell, and (laboratory) capillary waves. It is shown that the previously published decay rate models, which include either the effects due to an upper fluid or those due to interfacial contamination (but not both), are limiting cases of the present model. A parametric study of decay rate predictions shows that there are systems including ocean swell for which the influence of both the dynamics of the upper fluid and of the contamination are significant.