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arXiv2014

Diffuse Interface Methods for Multiple Phase Materials: An Energetic Variational Approach

In this paper, we introduce a diffuse interface model for describing the dynamics of mixtures involving multiple (two or more) phases. The coupled hydrodynamical system is derived through an energetic variational approach. The total energy of the system includes the kinetic energy and the mixing (interfacial) energies. The least action principle (or the principle of virtual work) is applied to derive the conservative part of the dynamics, with a focus on the reversible part of the stress tensor arising from the mixing energies. The dissipative part of the dynamics is then introduced through a dissipation function in the energy law, in line with the Onsager principle of least energy dissipation. The final system, formed by a set of coupled time-dependent partial differential equations, reflects a balance among various conservative and dissipative forces and governs the evolution of velocity and phase fields. To demonstrate the applicability of the proposed model, a few two-dimensional simulations have been carried out, including (1) the force balance at the three-phase contact line in equilibrium, (2) a rising bubble penetrating a fluid-fluid interface, and (3) a solid particle falling in a binary fluid. The effects of slip at solid surface have been examined in connection with contact line motion and a pinch-off phenomenon.

math.AP↗

arXiv2014

Numerical Study of Mechanism of U-shaped Vortex Formation

This paper illustrates the mechanism of U-shaped vortex formation which is found both by experiment and DNS. The main goal of this paper is to explain how the U-shaped vortex is formed and further develops. According to the results obtained by our direct numerical simulation with high order accuracy, the U-shaped vortex is part of the coherent vortex structure and is actually the tertiary streamwise vortices induced by the secondary vortices. The new finding is quite different from existing theories which describe that the U-shaped vortex is newly formed as the head of young turbulence spot and finally break down to small pieces. In addition, we find that the U-shaped vortex has the same vorticity sign as the original λ-shaped vortex tube legs and serves as a second neck to supply vorticity to the ringlike vortex when the original vortex tube is stretched and multiple rings are generated.

physics.flu-dyn↗

arXiv2014

LES Study on the Mechanism of Vortex Rings behind Supersonic MVG with Turbulent Inflow

In this study, we investigate the interaction between vortex rings behind MVG and the oblique shocks in the MVG controlled ramp flow at M=2.5 and Req=5760. Implicit large eddy simulation (ILES) method is used by solving the unfiltered form of the Navier-Stokes equations with the 5th order Bandwidth-optimized WENO scheme. The fully developed inflow is given by a series of turbulent profiles obtained from previous DNS simulation. It shows that the ring structure does not break down and keeps its topology after penetrating the strong shock wave and the oblique shocks is influenced a lot by the induced flow field from rings. The bump of the 3D shock wave surface is discovered and its mechanism is explained.

physics.flu-dyn↗

arXiv2014

Numerical and Experimental Studies on the Separation Topology of the MVG Controlled Flow at M=2.5

In this paper, the implicitly implemented LES method and fifth order bandwidth optimized WENO scheme are used to make comprehensive studies on the separation topology of the MVG controlled flow at M=2.5 and Reθ=5760. Experiments are also made to verify the prediction of the computation. Analyses are conducted on three categories of the topology: the surface separation, cross-section separation and the three dimensional structure of the vortices. A complete description about the separation topology and a series of new findings are obtained. Among them, a pair of spiral point is first predicted by the computation and verified by the experiment. A corresponding new vortex model with 7 vortex tubes is presented also.

physics.flu-dyn↗

arXiv2014

Numerical Study on Mechanism of Small Vortex Generation in Boundary Layer Transition

The small vortex generation is a key issue of the mechanism for late flow transition and turbulence generation. It was widely accepted that small length vortices were generated by large vortex breakdown. According to our recent DNS, we find that the hairpin vortex structure is very stable and never breaks down to small pieces. On the other hand, we recognize that there are strong positive spikes besides the ring neck in the spanwise direction. The strongly positive spikes are caused by second sweeps which are generated by perfectly circular and perpendicularly standing vortex rings. The second sweep brings energy from the invisid region downdraft to the bottom of the boundary layers, which generates high shear layers around the positive spikes.Since the high shear layer is not stable, all small length scales (turbulence) are generated around high shear layers especially near the wall surface (bottom of boundary layers). This happens near the ring neck in the streamwise direction and besides the original vortex legs in the spanwise direction.The small length scales then rise up from the wall surface and travel to the upper boundary layer.

physics.flu-dyn↗

arXiv2014

The Riemann Problem for Hyperbolic Equations under a Nonconvex Flux with Two Inflection Points

This report addresses the solution of Riemann problems for hyperbolic equations when the nonlinear characteristic fields loose their genuine nonlinearity. In this context, exact solvers for nonconvex 1D Riemann problems are developed. First a scalar conservation law for a nonconvex flux with two inflection points is studied. Then the P-system for an isothermal version of the van der Waals gas model is examined in a range of temperatures allowing for a nonconvex pressure function. Eventually the system of the Euler equations of gasdynamics is considered for the polytropic van der Waals gas. In this case, a suitably large specific heat is considered such that the isentropes display a local loss of convexity near the saturation curve and the critical point. Such a nonconvex physical model allows for nonclassical waves to appear as a result of the change of sign of the fundamental derivative of gasdynamics. The solution of the Riemann problem for the considered real gas model reduces to a system of two nonlinear equations for the values of the density on the two sides of the contact discontinuity, much in the same manner of a recently proposed solution method for gases admitting nonlinear wavefields only fully genuine. Solutions containing nonclassical and mixed waves are presented for the three mathematical models. Vacuum formation is described analytically including the presence of composite rarefaction waves, and to the best of authors knowledge, produced numerically here for the first time.

physics.flu-dyn↗

arXiv2014

The plasma protein fibrinogen stabilizes clusters of red blood cells in microcapillary flows

The supply of oxygen and nutrients and the disposal of metabolic waste in the organs depend strongly on how blood, especially red blood cells, flow through the microvascular network. Macromolecular plasma proteins such as fibrinogen cause red blood cells to form large aggregates, called rouleaux, which are usually assumed to be disaggregated in the circulation due to the shear forces present in bulk flow. This leads to the assumption that rouleaux formation is only relevant in the venule network and in arterioles at low shear rates or stasis. Thanks to an excellent agreement between combined experimental and numerical approaches, we show that despite the large shear rates present in microcapillaries, the presence of either fibrinogen or the synthetic polymer dextran leads to an enhanced formation of robust clusters of red blood cells, even at haematocrits as low as 1%. Robust aggregates are shown to exist in microcapillaries even for fibrinogen concentrations within the healthy physiological range. These persistent aggregates should strongly affect cell distribution and blood perfusion in the microvasculature, with putative implications for blood disorders even within apparently asymptomatic subjects.

physics.bio-ph↗

arXiv2014

DNS Study for the origin of the flow Randomization in Late Boundary Layer Transition

This paper is devoted to the investigation of the origin and mechanism of randomization in late boundary layer transition over a flat plate without pressure gradient. The flow randomization is a crucial phase before flow transition to the turbulent state. According to existing literatures, the randomization was caused by the big background noises and non-periodic spanwise boundary conditions. It was assumed that the large ring structure is affected by background noises first, and then the change of large ring structure affects the small length scales quickly, which directly leads to randomization and formation of turbulence. However, by careful analysis of our high order DNS results, we believe that the internal instability of multiple ring cycles structure is the main reason. What we observed is that randomization begins when the third cycle overlaps the first and second cycles. A significant asymmetric phenomenon is originated from the second cycle in the middle of both streamwise and spanwise directions. More technically, a visible asymmetric phenomenon in the middle vortex ring cycle starts at time step t=16.25T and x=838.9δin where the top and bottom level rings are still completely symmetric. The non-symmetric structure of middle level ring affects the small length scale in boundary layer bottom quickly. The randomization phenomenon spreads to top level through ejections. Finally, the whole flow domain becomes randomized. A hypothesis of C- and K-types shift is given as a possible mechanism of flow randomization.

nlin.CD↗

arXiv2014

DNS Study on Physics of Late Boundary Layer Transition

This paper serves as a review of our recent new DNS study on physics of late boundary layer transition. This includes mechanism of the large coherent vortex structure formation, small length scale generation and flow randomization. The widely spread concept vortex breakdown to turbulence,which was considered as the last stage of flow transition, is not observed and is found theoretically incorrect. The classical theory on boundary layer transition is challenged and we proposed a new theory with five steps, i.e. receptivity, linear instability, large vortex formation, small length scale generation, loss of symmetry and randomization to turbulence. We have also proposed a new theory about turbulence generation. The new theory shows that all small length scales (turbulence) are generated by shear layer instability which is produced by large vortex structure with multiple level vortex rings, multiple level sweeps and ejections, and multiple level negative and positive spikes near the laminar sub-layers.Therefore, turbulence is not generated by vortex breakdown but rather positive and negative spikes and consequent high shear layers. Shear layer instability is considered as the mother of turbulence. This new theory may give a universal mechanism for turbulence generation and sustenance which shows that the energy is brought by large vortex structure through multiple level sweeps.

physics.flu-dyn↗

arXiv2014

Controlled topological transitions in thin film phase separation

In this paper the evolution of a binary mixture in a thin-film geometry with a wall at the top and bottom is considered. By bringing the mixture into its miscibility gap so that no spinodal decomposition occurs in the bulk, a slight energetic bias of the walls towards each one of the constituents ensures the nucleation of thin boundary layers that grow until the constituents have moved into one of the two layers. These layers are separated by an interfacial region where the composition changes rapidly. Conditions that ensure the separation into two layers with a thin interfacial region are investigated based on a phase-field model. Using matched asymptotic expansions a corresponding sharp-interface problem for the location of the interface is established. It is then argued that this newly created two-layer system is not at its energetic minimum but destabilizes into a controlled self-replicating pattern of trapezoidal vertical stripes by minimizing the interfacial energy between the phases while conserving their area. A quantitative analysis of this mechanism is carried out via a thin-film model for the free interfaces, which is derived asymptotically from the sharp-interface model.

physics.flu-dyn↗

arXiv2014

Statistical Properties of the Intrinsic Geometry of Heavy-particle Trajectories in Two-dimensional, Homogeneous, Isotropic Turbulence

We obtain, by extensive direct numerical simulations, trajectories of heavy inertial particles in two-dimensional, statistically steady, homogeneous, and isotropic turbulent flows, with friction. We show that the probability distribution function $\mathcal{P}(κ)$, of the trajectory curvature $κ$, is such that, as $κ\to \infty$, $\mathcal{P}(κ) \sim κ^{-h_{\rm r}}$, with $h_{\rm r} = 2.07 \pm 0.09$. The exponent $h_{\rm r}$ is universal, insofar as it is independent of the Stokes number ($\rm{St}$) and the energy-injection wave number. We show that this exponent lies within error bars of their counterparts for trajectories of Lagrangian tracers. We demonstrate that the complexity of heavy-particle trajectories can be characterized by the number $N_{\rm I}(t,{\rm St})$ of inflection points (up until time $t$) in the trajectory and $n_{\rm I} ({\rm St}) \equiv \lim_{t\to\infty} \frac{N_{\rm I} (t,{\rm St})}{t} \sim {\rm St}^{-Δ}$, where the exponent $Δ= 0.33 \pm0.02$ is also universal.

physics.flu-dyn↗

arXiv2014

Numerical and experimental modeling of mixing of impinging jets radially injected into crossflow

In some chemical processes, the formation of the counter flow in the colliding-jets regime is the most promising phenomenon if there is a need of fast quenching of an obtained product [1]. Particularly this method can be used to control disperse and phase composition of the final product. The complex calculation and experimental research of the counter collision and mixing of the circular argon jet and aluminum steams at 2000 K, and a relative cold argon jet (1000 K) is presented in [2]. It is shown there that the counter quenching regime enables to control particles grow owing to the flow dilution with the quenching jet and variation of the temperature drop rate.

physics.flu-dyn↗

arXiv2014

Thermodynamically consistent modeling for dissolution/growth of bubbles in an incompressible solvent

We derive mathematical models of the elementary process of dissolution/growth of bubbles in a liquid under pressure control. The modeling starts with a fully compressible version, both for the liquid and the gas phase so that the entropy principle can be easily evaluated. This yields a full PDE system for a compressible two-phase fluid with mass transfer of the gaseous species. Then the passage to an incompressible solvent in the liquid phase is discussed, where a carefully chosen equation of state for the liquid mixture pressure allows for a limit in which the solvent density is constant. We finally provide a simplification of the PDE system in case of a dilute solution.

physics.flu-dyn↗

arXiv2014

Influence of small scale magnetic energy and helicity on the growth of large scale magnetic field

The influence of initially given small scale magnetic energy($E_M(0)$) and helicity($H_M(0)$) on the magnetohydrodynamics(MHD) dynamo was investigated. Equations for $E_M$(t), $H_M$(t), and electromotive force($\langle {\bf v}\times {\bf b}\rangle$, $EMF$) were derived and solved. The solutions indicate small scale magnetic field(${\bf b}_i$) caused by $E_M$(0) modifies $EMF$ and generates additional terms of which effect depends on magnetic diffusivity $η$, position of initial conditions($IC$s) $k_f$, and time ($\sim e^{-ηk_f^2 t}$). ${\bf b}_i$ increases the inverse cascade of energy resulting in the enhanced growth of large scale magnetic field($\overline{\bf B}$). Simulation data show that $E_M$(0) in small scale boosts the growth rate, which also proportionally depends on $H_M(0)$. If $E_M$(0) is the same, positive $H_M(0)$ is more effective for MHD dynamo than negative $H_M(0)$ is. It was discussed why large scale magnetic helicity should have the opposite sign of the injected kinetic helicity.

astro-ph.SR↗

arXiv2014

Inertial wave and zonal flow in librating spherical shells

We numerically study the inertial waves and zonal flows in spherical shells driven by longitudinal libration, an oscillatory variation of rotation rate. Internal shear layers are generated due to breakdown of the Ekman boundary layer at critical latitudes. Our numerical results validate the scaling laws of internal shear layers predicted by previous studies. Mean zonal flows are driven by the non-linear interaction in the boundary layers. Non-linear interaction of inertial waves in the interior fluids has no significant contribution to the zonal flow. Multiple geostrophic shear layers are generated due to non-linearities in the boundary layers at critical latitudes and reflection points of internal shear layers. We also investigate the scaling laws of geostrophic shear layers and extrapolate the results to the planetary setting.

physics.flu-dyn↗

arXiv2014

A predicable condition for boundary layer separation of 2-D incompressible fluid flows

In this paper, the solutions of Navier-Stokes equations with Dirichlet boundary conditions governing 2-D incompressible fluid flows are considered. A condition for boundary layer separation, which is determined by initial values and external forces, is obtained. More importantly, the condition can predict directly when and where boundary layer separation will occur. The main technical tool is geometric theory of incompressible flows developed by T. Ma and S.Wang.

physics.flu-dyn↗

arXiv2014

Benchmarking in a rotating annulus: a comparative experimental and numerical study of baroclinic wave dynamics

The differentially heated rotating annulus is a widely studied tabletop-size laboratory model of the general mid-latitude atmospheric circulation. The two most relevant factors of cyclogenesis, namely rotation and meridional temperature gradient are quite well captured in this simple arrangement. The radial temperature difference in the cylindrical tank and its rotation rate can be set so that the isothermal surfaces in the bulk tilt, leading to the formation of baroclinic waves. The signatures of these waves at the free water surface have been analyzed via infrared thermography in a wide range of rotation rates (keeping the radial temperature difference constant) and under different initial conditions. In parallel to the laboratory experiments, five groups of the MetStröm collaboration have conducted numerical simulations in the same parameter regime using different approaches and solvers, and applying different initial conditions and perturbations. The experimentally and numerically obtained baroclinic wave patterns have been evaluated and compared in terms of their dominant wave modes, spatio-temporal variance properties and drift rates. Thus certain ``benchmarks'' have been created that can later be used as test cases for atmospheric numerical model validation.

physics.flu-dyn↗

arXiv2014

The effect of Prandtl number on mixing in low Reynolds number Kelvin-Helmholtz billows

The effect of Prandtl number on the evolution of Kelvin-Helmholtz (KH) billows and the amount of mixing they generate is studied through direct numerical simulation (DNS). The results indicate that the time evolution of the rate of mixing through different stages of the life-cycle of KH flow is significantly influenced by the Prandtl number. As the Prandtl number increases, the final amount of mixing increases for Reynolds that are too low to support active three-dimensional motions. This trend is the opposite in sufficiently high Reynolds number KH flows that can overcome viscous effects, and develop significant three-dimensional instabilities. While the mixing generated in the two-dimensional flows, uniform in the span-wise direction, is not significantly dependent on the Prandtl number, the turbulent mixing induced by three-dimensional motions is a function of the Prandtl number. The turbulent mixing efficiency near the end of the turbulence decay phase approaches 0.2, the commonly observed value in the ocean. A smooth transition in mixing is observed by increasing the buoyancy Reynolds number.

physics.flu-dyn↗