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Register a new userFinite Domain Anomalous Spreading Consistent with First and Second Law
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After reviewing the problematic behavior of some previously suggested finite interval spatial operators of the symmetric Riesz type, we create a wish list leading toward a new spatial operator suitable to use in the space-time fractional differential equation of anomalous diffusion when the transport of material is strictly restricted to a bounded domain. Based on recent studies of wall effects, we introduce a new definition of the spatial operator and illustrate its favorable characteristics. We provide two numerical methods to solve the modified space-time fractional differential equation and show particular results illustrating compliance to our established list of requirements, most important to the conservation principle and the second law of thermodynamics.
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Floating offshore structures often exhibit low-frequency oscillatory motions in the horizontal plane, with amplitudes in the same order as their characteristic dimensions and larger than the corresponding wave-frequency responses, making the traditional formulations in an inertial coordinate system inconsistent and less applicable. To address this issue, we explore an alternative formulation completely based on a non-inertial body-fixed coordinate system. Unlike the traditional seakeeping models, this formulation consistently allows for large-amplitude horizontal motions. A numerical model based on a higher-order boundary element is applied to solve the resulting boundary-value problems in the time domain. A new set of explicit time-integration methods, which do not necessitate the use of upwind schemes for spatial derivatives, are designed to deal with the convective-type free-surface conditions. To suppress the weak saw-tooth instabilities on the free surface in time marching, we also present novel low-pass filters based on optimized weighted-least-squares, which are in principle applicable for both structured and unstructured meshes. For ship seakeeping and added resistance analyses, we show that the present computational model does not need to use soft-springs for surge and sway, in contrast to the traditional models. For a spar floating offshore wind turbine (FOWT), the importance of consistently taking into account the effects of large horizontal motions is demonstrated considering the bi-chromatic incident waves. The present model is also referred to as a complete 2nd order wave-load model, as all the 2nd order wave loads, including the sum-frequency and difference-frequency components, are solved simultaneously.
We present high-precision experimental and numerical studies of the Nusselt number $Nu$ as functions of the Rayleigh number $Ra$ in geostrophic rotating convection with domain aspect ratio ${Gamma}$ varying from 0.4 to 3.8 and the Ekman number Ek from $2.0{times}10^{-7}$ to $2.7{times}10^{-5}$. The heat-transport data $Nu(Ra)$ reveal a gradual transition from buoyancy-dominated to geostrophic convection at large $Ek$, whereas the transition becomes sharp with decreasing $Ek$. We determine the power-law scaling of $Nu{sim}Ra^{gamma}$, and show that the boundary flows give rise to pronounced enhancement of $Nu$ in a broad range of the geostrophic regime, leading to reduction of the scaling exponent ${gamma}$ in small ${Gamma}$ cells. The present work provides new insight into the heat-transport scaling in geostrophic convection and may explain the discrepancies observed in previous studies.
Immiscible fluid-fluid displacement in porous media is of great importance in many engineering applications, such as enhanced oil recovery, agricultural irrigation, and geologic CO2 storage. Fingering phenomena, induced by the interface instability, are commonly encountered during displacement processes and somehow detrimental since such hydrodynamic instabilities can significantly reduce displacement efficiency. In this study, we report a possible adjustment in pore geometry which aims to suppress the capillary fingering in porous media with hierarchical structures. Through pore-scale simulations and theoretical analysis, we demonstrate and quantify combined effects of wettability and hierarchical geometry on displacement patterns, showing a transition from fingering to compact mode. Our results suggest that with a higher porosity of the 2nd-order porous structure, the displacement can keep compact across a wider range of wettability conditions. Combined with our previous work on viscous fingering in such media, we can provide a complete insight into the fluid-fluid displacement control in hierarchical porous media, across a wide range of flow conditions from capillary- to viscous-dominated modes. The conclusions of this work can benefit the design of microfluidic devices, as well as tailoring porous media for better fluid displacement efficiency at the field scale.
Viscous heating can play an important role in the dynamics of fluids with strongly temperature-dependent viscosities because of the coupling between the energy and momentum equations. The heat generated by viscous friction produces a local temperature increase near the tube walls with a consequent decrease of the viscosity and a strong stratification in the viscosity profile. The problem of viscous heating in fluids was investigated and reviewed by Costa & Macedonio (2003) because of its important implications in the study of magma flows. Because of the strong coupling between viscosity and temperature, the temperature rise due to the viscous heating may trigger instabilities in the velocity field, which cannot be predicted by a simple isothermal Newtonian model. When viscous heating produces a pronounced peak in the temperature profile near the walls, a triggering of instabilities and a transition to secondary flows can occur because of the stratification in the viscosity profile. In this paper we focus on the thermal and mechanical effects caused by viscous heating. We will present the linear stability equations and we will show, as in certain regimes, these effects can trigger and sustain a particular class of secondary rotational flows which appear organised in coherent structures similar to roller vortices. This phenomenon can play a very important role in the dynamics of magma flows in conduits and lava flows in channels and, to our knowledge, it is the first time that it has been investigated by a direct numerical simulation.
This paper represents a theoretical and an experimental study of the spreading dynamics of a liquid droplet, generated by a needle free deposition system called the liquid needle droplet deposition technique. This technique utilizes a continuous liquid jet generated from a pressurized dosing system which generates a liquid drop on a substrate to be characterized by optical contact angle measurements. Although many studies have explored the theoretical modelling of the droplet spreading scenario, a theoretical model representing the spreading dynamics of a droplet, generated by the jet impact and continuous addition of liquid mass, is yet to be addressed. In this study, we developed a theoretical model based on the overall energy balance approach which enables us to study on the physics of variation of droplet spreading under surrounding medium of various viscosities. The numerical solution of the non-linear ordinary differential equation has provided us the opportunity to comment on the variation of droplet spreading, as a function of Weber number ($We$), Reynolds number ($Re$) and Bond number ($Bo$) ranging from 0.5-3, 75-150, and 0.001-0.3, respectively. We have also presented a liquid jet impact model in order to predict the initial droplet diameter as an initial condition for the proposed governing equation. The model has been verified further with the experimental measurements and reasonable agreement has been observed. Experimental observations and theoretical investigations also highlight the precision, repeatability and wide range of the applicability of liquid needle drop deposition technique.
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