A physically-based method to derive well-posed instances of the two-fluid transport equations for two-phase flow, from the Hamilton principle, is presented. The state of the two-fluid flow is represented by the superficial velocity and the drift-flux, instead of the average velocities of each fluid. This generates the conservation equations of the two principal motion modes naturally: the global center-of-mass flow and the relative velocity between fluids. Well-posed equations can be obtained by modelling the storage of kinetic energy in fluctuations structures induced by the interaction between fluids, like wakes and vortexes. In this way, the equations can be regularized without losing in the process the instabilities responsible for flow-patterns formation and transition. A specific case of vertical air-water flow is analyzed showing the capability of the present model to predict the formation of the slug flow regime as trains of non-linear waves.
Laminar natural convection from two horizontally aligned isothermal cylinders in unconfined Power-law fluids has been investigated numerically. The effect of horizontal spacing (0<=(S/D)<=10) on both momentum and heat transfer characteristics has been delineated under the following pertinent parameters: Grashof number (10<=Gr<=1e3), Prandtl number (0.71<=n<=100), and Power-law index (0.4<=n<=1.6). The heat transfer characteristics are elucidated in terms of isotherms, local Nusselt number (Nu) distributions and average Nusselt number values, whereas the flow characteristics are interpreted in …
In high head Francis turbines and pump-turbines in particular, Rotor Stator Interaction (RSI) is an unavoidable source of excitation that needs to be predicted accurately. Precise knowledge of turbine dynamic characteristics, notably the variation of the rotor natural frequencies with rotation speed and added mass of the surrounding water, is essential to assess potential resonance and resulting amplification of vibrations. In these machines, the disk-like structures of the runner crown and band as well as the head cover and bottom ring give rise to the emergence of diametrical modes and a mod…
The velocity-vorticity correlation integral (Chkhetiani invariant) is an invariant of a viscous Karman-Howarth equation. In the tree-dimensional space this invariant can naturally determine a turbulent diffusivity (viscosity). It is shown, using results of direct numerical simulations, that distributed chaos dominated by this integral can provide an adequate description of the turbulent Rayleigh-Bénard convection, stably stratified turbulence and Rayleigh-Taylor mixing at Prandtl number $Pr \sim 1$.
Severe contradictions exist between experimental observations and computational predictions regarding natural convective thermal transport in nanosuspensions. The approach treating nanosuspensions as homogeneous fluids in computations has been pin pointed as the major contributor to such contradictions. To fill the void, inter particle and particle fluid interactivities (slip mechanisms), in addition to effective thermophysical properties, have been incorporated within the present formulation. Through thorough scaling analysis, the dominant slip mechanisms have been identified. A Multi Compone…
The present work numerically investigates the influence of radiation on the natural convection in differentially heated slender and square-base tall cavities at low operating temperature range of 288.1-307.7 K. The atmospheric air which has the composition of $N_2$, $O_2$, $CO_2$ and $H_2O$ in the molar mass proportion of 75.964%, 21%, 0.036% and 3%, respectively, has been considered as the working fluid in the cavities. The non-gray and gray Planck mean absorption coefficients for whole spectrum of the air at the atmospheric pressure and average temperature of the cavity have been calculated …
We discuss heat conductivity from the point of view of a variational multi-fluid model, treating entropy as a dynamical entity. We demonstrate that a two-fluid model with a massive fluid component and a massless entropy can reproduce a number of key results from extended irreversible thermodynamics. In particular, we show that the entropy entrainment is intimately linked to the thermal relaxation time that is required to make heat propagation in solids causal. We also discuss non-local terms that arise naturally in a dissipative multi-fluid model, and relate these terms to those of phonon hydr…
Analysis of conjugate natural convection with surface radiation in a two-dimensional enclosure is carried out in order to search the optimal location of the heat source with entropy generation minimization (EGM) approach and conventional heat transfer parameters. The air as an incompressible fluid and transparent media is considered the fluid filling the enclosure with the steady and laminar regime. The enclosure internal surfaces are also gray, opaque and diffuse. The governing equations with stream function and vorticity formulation are solved using finite difference approach. Results includ…
In the present work, the effects of diffuse and collimated radiation on the symmetrical cooling case of natural convection in a two-dimensional cavity heated from the bottom have been investigated, numerically. The cavity is convectively heated from the bottom with heat transfer coefficient of 50 W/m2K and free stream temperature 305 K, while both vertical walls of cavity are isothermal at temperature of 296 K. The top wall is adiabatic and all walls are opaque for radiation heat transfer. For collimated case, a small semitransparent window of non-dimensional width of 0.05 at height of 0.7 has…
We study the velocity field in a horizontal (x-y) plane 1.5 mm above the hot plate in turbulent natural convection using PIV at a Rayleigh number Raw=106 and Prandtl number Pr=5.2. The plane of measurement is inside the velocity boundary layer estimated from the natural convection boundary layer equations[7] as well as inside the velocity boundary layer due to the large scale flow[2, 5].The boundary layer comprises of line plumes with sinking fluid between them. The instantaneous velocity variation from the center of the sinking fluid to the line plumes is found to deviate with the classical P…
In this study, we present a global Fourier mode decomposition framework for unsteady fluid-structure interaction. We apply the framework to isolate and extract the aeroelastic modes arising from a coupled three-dimensional fluid-membrane system. The proposed framework is employed to decompose the physical variables in the fluid and structural domains into frequency-ranked aeroelastic modes in a unified way. We observe the frequency synchronization between the vortex shedding and the structural vibration via mode decomposition analysis. We examine the role of flexibility in the aeroelastic mode…
Capillary phenomena are involved in many industrial processes, especially those dealing with composite manufacturing. However, their modelling is still challenging. Therefore, a finite element setting is proposed to better investigate this complex issue. The variational formulation of a liquid-air Stokes system is established, while the solid substrate is described through boundary conditions. Expressing the weak form of Laplace's law over liquid-air, liquid-solid and air-solid interfaces, leads to a natural enforcement of the mechanical equilibrium over the wetting line, without imposing expl…
A kind of problems of radially symmetric transient fluid flow in a medium with a geometry similar to a hollow-disk can be addressed using the finite Hankel transform. However, the inverse Hankel transform [G. Cinelli, Int. J. Engng. Sci., 3, 539 (1965)] works well only for homogeneous boundary conditions. We use the finite Hankel transform, together with the Laplace transform, to solve partial dfferential equations with inhomogeneous boundary conditions. With this aim, we propose a method to obtain an analytical solution of the problem of fluid flow in a finite naturally fractured reservoir wi…
The rotational dynamics of anisotropic particles advected in a turbulent fluid flow are important in many industrial and natural setting. Particle rotations are controlled by small scale properties of turbulence that are nearly universal, and so provide a rich system where experiments can be directly compared with theory and simulations. Here we report the first three-dimensional experimental measurements of the orientation dynamics of rod-like particles as they are advected in a turbulent fluid flow. We also present numerical simulations that show good agreement with the experiments and allow…
A natural framework for isogeometric fluid-structure interaction based on BEM-shell coupling
SISSA-International School for Advanced Studies（国际高等研究院）；Technische Universität Braunschweig（布伦瑞克工业大学）；University of Pavia（帕维亚大学）；Technische Universität München（慕尼黑工业大学）
In this paper, we present a novel approach to model the fluid/solid interaction forces in a direct solver of the Navier-Stokes equations based on the volume of fluid interface tracking method. The key ingredient of the model is the explicit inclusion of the fluid/solid interaction forces into the governing equations. We show that the interaction forces lead to a partial wetting condition and in particular to a natural definition of the equilibrium contact angle. We present two numerical methods to discretize the interaction forces that enter the model; these two approaches differ in complexity…
A starting plume or jet has a well-defined, evolving head that is driven through the surrounding quiescent fluid by a localized flux of either buoyancy or momentum, or both. We studied the scaling and morphology of starting plumes produced by a constant flux of buoyant fluid from a small, submerged outlet. The plumes were laminar and spanned a wide range of plume Richardson numbers Ri. Ri is the dimensionless ratio of the buoyancy forces to inertial effects, and is thus our measurements crossed over the transition between buoyancy-driven plumes and momentum-driven jets. We found that the ascen…
The mathematical formulation, basic concept and numerical implementation of a new meshless method for solving three dimensional fluid flow and related heat transfer problems are presented in this paper. Moving least squares approximation is used for the spatial discretization together with an implicit scheme for time marching. The vorticity and vector potential formulation of Navier-Stokes equations is employed to avoid the difficulties associated with pressure/velocity coupling. Two 3D problem of natural convection in a differentially heated cubic cavity and in the annular space between a sph…
Immiscible fluid displacement in porous media is fundamental for many environmental processes, including infiltration of water in soils, groundwater remediation, enhanced recovery of hydrocarbons and carbon geosequestration. Microstructural heterogeneity, in particular of particle sizes, can significantly impact immiscible displacement. For instance, it may lead to unstable flow and preferential displacement patterns. We present a systematic, quantitative pore-scale study of the impact of spatial correlations in particle sizes on the drainage of a partially-wetting fluid. We perform pore-netwo…
The dissolution of solids has created spectacular geomorphologies ranging from centimeter-scale cave scallops to the kilometer-scale "stone forests" of China and Madagascar. Mathematically, dissolution processes are modeled by a Stefan problem, which describes how the motion of a phase-separating interface depends on local concentration gradients, coupled to a fluid flow. Simulating these problems is challenging, requiring the evolution of a free interface whose motion depends on the normal derivatives of an external field in an ever-changing domain. Moreover, density differences created in th…
We consider a model of a third grade viscous Korteweg--type fluid in three space dimensions, and apply the extended Liu procedure in order to explicitly solve the constraints imposed by the entropy principle on the non--local constitutive relations. We detail the algorithm we use, and are able to characterize the material functions involved in the constitutive equations. In a natural way, the application of the extended Liu procedure allows us to recover an extra term in the entropy flux, preserving all the features of third grade viscous Korteweg--type fluids. Moreover, a further constraint, …
The interaction of flexible polymers with fluid flows leads to a number of intriguing phenomena observed in laboratory experiments, namely drag reduction, elastic turbulence and heat transport modification in natural convection, and is one of the most challenging subjects in soft matter physics. In this paper we review our present knowledge on the subject. Our present knowledge is mostly based on direct numerical simulations performed in the last twenty years, which have successfully explained, at least qualitatively, most of the experimental results. Our goal is to disentangle as much as poss…
A simplified model of natural convection, similar to the Lorenz (1963) system, is compared to computational fluid dynamics simulations in order to test data assimilation methods and better understand the dynamics of convection. The thermosyphon is represented by a long time flow simulation, which serves as a reference "truth". Forecasts are then made using the Lorenz-like model and synchronized to noisy and limited observations of the truth using data assimilation. The resulting analysis is observed to infer dynamics absent from the model when using short assimilation windows. Furthermore, cha…
Simons Center for Geometry and Physics, Yang Institute for Theoretical Physics, Stony Brook（石溪大学西蒙斯几何与物理中心、杨理论物理研究所）；Leinweber Institute for Theoretical Physics, Kadanoff Center for Theoretical Physics and Enrico Fermi Institute, University of Chicago（芝加哥大学莱因韦伯理论物理研究所、卡达诺夫理论物理中心及恩里科费米研究所）
Nonlinear waves in defocusing media are investigated in the framework of the hydrodynamic description of light as a photon fluid. The observations are interpreted in terms of an emergent curved spacetime generated by the waves themselves, which fully determines their dynamics. The spacetime geometry emerges naturally as a result of the nonlinear interaction between the waves and the self-induced background flow. In particular, as observed in real fluids, different points of the wave profile propagate at different velocities leading to the self-steepening of the wave front and to the formation …
We present a natural framework for studying the persistence problem in two-dimensional fluid turbulence by using the Okubo-Weiss parameter $Λ$ to distinguish between vortical and extensional regions. We then use a direct numerical simulation (DNS) of the two-dimensional, incompressible Navier--Stokes equation with Ekman friction to study probability distribution functions (PDFs) of the persistence times of vortical and extensional regions by employing both Eulerian and Lagrangian measurements. We find that, in the Eulerian case, the persistence-time PDFs have exponential tails; by contrast, th…
A perturbative method called beatification is presented for a class of two-dimensional fluid and plasma theories. The Hamiltonian systems considered, namely the Euler, Vlasov-Poisson, Hasegawa-Mima, and modified Hasegawa-Mima equations, are naturally described in terms of noncanonical variables. The beatification procedure amounts to finding the correct transformation that removes the explicit variable dependence from a noncanonical Poisson bracket and replaces it with a fixed dependence on a chosen state in phase space. As such, beatification is a major step toward casting the Hamiltonian sys…
