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arXiv2018

Investigation of cloud cavitation passive control method for hydrofoils using Cavitating-bubble Generators (CGs)

In this article, we propose a passive method to control unsteady cloud cavitation on hydrofoils using cavitation-bubble generator (CGs). This method may be used in many engineering applications, in particular in marine and turbomachinery. First, we used a Partially-averaged Navier Stokes (PANS) model for turbulence to simulate the unsteady cavitating flow and validated it based on experimental data. This model was coupled with a mass transfer model and implemented to the open source software package OpenFOAM. Second, the effect of a proper design of CGs on qualitative parameters such as cavitation structure and the shape of cavity were studied. The effect of CGs on the destructive effects of cavitation such as vibration, turbulent velocity fluctuations and high- pressure amplitude were analyzed. Our results showed that a proper design of CGs may reduce the amplitude of the force fluctuations on the hydrofoil substantially. Further on, the local boundary layer around the hydrofoil surface was altered and the turbulent velocity fluctuation was reduced significantly using this technique.

physics.flu-dyn↗

arXiv2018

Instability-driven Oscillations of Elastic Microfilaments

Cilia and flagella are highly conserved slender organelles that exhibit a variety of rhythmic beating patterns from non-planar cone-like motions to planar wave-like deformations. Although their internal structure, composed of a microtubule-based axoneme driven by dynein motors, is known, the mechanism responsible for these beating patterns remains elusive. Existing theories suggest that the dynein activity is dynamically regulated, via a geometric feedback from the cilium's mechanical deformation to the dynein force. An alternative, open-loop mechanism based on a 'flutter' instability was recently proven to lead to planar oscillations of elastic filaments under follower forces. Here, we show that an elastic filament in viscous fluid, clamped at one end and acted on by an external distribution of compressive axial forces, exhibits a Hopf bifurcation that leads to non-planar spinning of the buckled filament at a locked curvature. We also show the existence of a second bifurcation, at larger force values, that induces a transition from non-planar spinning to planar wave-like oscillations. We elucidate the nature of these instabilities using a combination of nonlinear numerical analysis, linear stability theory, and low-order bead-spring models. Our results show that away from the transition thresholds, these beating patterns are robust to perturbations in the distribution of axial forces and in the filament configuration. These findings support the theory that an open-loop, instability-driven mechanism could explain both the sustained oscillations and the wide variety of periodic beating patterns observed in cilia and flagella.

physics.flu-dyn↗

arXiv2018

The new mode of instability in viscous high-speed boundary layer flows

The new mode of instability found by Tunney et al. is studied with viscous stability theory in this article. When the high-speed boundary layer is subject to certain values of favorable pressure gradient and wall heating, a new mode becomes unstable due to the appearance of the streamwise velocity overshoot ($U(y)>U_\infty$) in the base flow. The present study shows that under practical Reynolds numbers, the new mode can hardly co-exist with conventional first mode and Mack's second mode. Due to the requirement for additional wall heating, the new mode may only lead to laminar-turbulent transition under experimental (artificial) conditions.

physics.flu-dyn↗

arXiv2018

On Diffusion-Induced Non-Constant Composition Profiles in the Boundary Layer of Inert Multicomponent Mixtures

In the boundary layer of multicomponent fluid mixtures, the species-specific mass flux in the wall-normal direction is determined by the combination of turbulent-diffusiophoretic diffusion due to composition gradients, and diffusion due to gradients in other scalar fields (e.g. thermophoresis, barophoresis, and forced diffusion). For inert mixtures, a balance must exist between all the diffusive transport mechanisms so that the net diffusive mass flux normal to the wall is zero everywhere. This paper discusses under which conditions non-constant composition profiles are necessary to obtain physico-chemical equilibrium, hence vanishing transport, in the wall-normal direction. Mathematical modeling is employed to demonstrate how this may affect fluid property profiles, wall heat flux, and wall shear stress in an ideal, ternary gas mixture ($H_2 + N_2 + CO_2$) subject to a temperature gradient. It is concluded that competing diffusive transport mechanisms, under certain circumstances, may result in non-constant composition profiles and significantly different wall and bulk compositions, for inert multicomponent mixtures. Hence, wall-normal diffusion in the boundary layer must be accounted for to correctly describe or interpret multicomponent flow systems sensitive to wall friction and heat exchange.

physics.flu-dyn↗

arXiv2018

Convolutions on the Sphere: Commutation with Differential Operators

We generalize the definition of convolution of vectors and tensors on the 2-sphere, and prove that it commutes with differential operators. Moreover, vectors and tensors that are normal/tangent to the spherical surface remain so after the convolution. These properties make the new filtering operation particularly useful to analyzing and modeling nonlinear dynamics in spherical systems, such as in geophysics, astrophysics, and in inertial confinement fusion applications. An essential tool we use is the theory of scalar, vector, and tensor spherical harmonics. We then show that our generalized filtering operation is equivalent to the (traditional) convolution of scalar fields of the Helmholtz decomposition of vectors and tensors.

math-ph↗

arXiv2019

Analytical solutions from integral transforms for transient fluid flow in naturally fractured porous media with and without boundary flux

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 with inner and outer boundaries having constant and time-dependent conditions, respectively. We assume that the reservoir has a producing well, with either constant terminal pressure or constant terminal rate, while the outer boundary has either an influx recharge or constant pressure. Using these case studies, we show that a part of the inverse transformation given by Cinelli can be expressed as closed formulas for long time solutions, at the same time that make it possible to capture the inhomogeneous condition and speed up the convergence of solutions. For Neumann-Neumann conditions, we show that the inverse expression of Cinelli is incomplete. In addition, an analysis of the flow characteristic curves in a reservoir with influx recharge is presented. The drawdown pressure curves are used to elucidate the statement that the pressure drop of a single-porosity reservoir with influx recharge resembles the flow behavior in a double-porosity closed reservoir, establishing a criteria to distinguish between both.

math.AP↗

arXiv2018

Parametric mechanism maintaining Couette flow turbulence verified in DNS implies novel control strategies

The no-slip boundary condition results in a velocity shear forming in fluid flow near a solid surface. This shear flow supports the turbulence characteristic of fluid flow near boundaries at Reynolds numbers above $\approx1000$ by making available to perturbations the kinetic energy of the externally forced flow. Understanding the physical mechanism underlying this energy transfer poses a fundamental question. Although qualitative understanding that this transfer involves nonlinear destabilization of the roll-streak coherent structure has been established, identification of this instability has resisted analysis. The reason this instability has resisted analysis is that its analytic expression lies in the Navier-Stokes equations (NS) expressed using statistical rather than state variables. Expressing NS as a statistical state dynamics (SSD) at second order in a cumulant expansion suffices to allow analytical identification of the nonlinear roll-streak instability underlying turbulence in wall-bounded shear flow. In this nonlinear instability the turbulent perturbation field is identified by the SSD with the Lyapunov vectors of the linear operator governing perturbation evolution about the time-dependent streamwise mean flow. In this work, the implications of the predictions of SSD analysis (that this parametric instability underlies the dynamics of turbulence in Couette flow and that the perturbation structures are the associated Lyapunov vectors) are interpreted to imply new conceptual approaches to controlling turbulence. It is shown that the perturbation component of turbulence is supported on the streamwise mean flow, which implies optimal control should be formulated to suppress perturbations from the streamwise mean. It is also shown that suppressing only the top few Lyapunov vectors on the streamwise mean vectors results in laminarization. These results are verified using DNS.

physics.flu-dyn↗

arXiv2018

Global Existence of Weak Solutions to the Compressible Primitive Equations of Atmospheric Dynamics with Degenerate Viscosities

We show the existence of global weak solutions to the three-dimensional compressible primitive equations of atmospheric dynamics with degenerate viscosities. In analogy with the case of the compressible Navier-Stokes equations, the weak solutions satisfy the basic energy inequality, the Bresh-Desjardins entropy inequality and the Mellet-Vasseur estimate. These estimates play an important role in establishing the compactness of the vertical velocity of the approximating solutions, and therefore are essential to recover the vertical velocity in the weak solutions.

math.AP↗

arXiv2018

CUBE: A scalable framework for large-scale industrial simulations

Writing high performance solvers for engineering applications is a delicate task. These codes are often developed on an application to application basis, highly optimized to solve a certain problem. Here, we present our work on developing a general simulation framework for efficient computation of time resolved approximations of complex industrial flow problems - Complex Unified Building cubE method (Cube). To address the challenges of emerging, modern supercomputers, suitable data structures and communication patterns are developed and incorporated into Cube. We use a Cartesian grid together with various immersed boundary methods to accurately capture moving, complex geometries. The asymmetric workload of the immersed boundary is balanced by a predictive dynamic load balancer, and a multithreaded halo-exchange algorithm is employed to efficiently overlap communication with computations. Our work also concerns efficient methods for handling the large amount of data produced by large-scale flow simulations, such as scalable parallel I/O, data compression and in-situ processing.

cs.CE↗

arXiv2018

Electrohydrodynamics of compound droplet in a microfluidic confinement

The present study deals with the dynamics of a double emulsion confined in a microchannel under the presence of a uniform electric field. Towards investigating the non-trivial electrohydrodynamics of a compound droplet, confined in between two parallel plate electrodes, a phase field approach has been adopted. Under the assumption of negligible fluid inertia and small shape deformation, an asymptotic model is also developed to predict the transient as well as the steady state droplet dynamics in the limiting case of an unbounded suspending medium. The phases involved are either assumed to be perfect dielectric or leaky dielectric. Subsequent investigation shows that shape deformation of either of the interfaces of the droplet increase with rise in the channel confinement for a perfect dielectric system. However, for a leaky dielectric system, the deformation of inner droplet and outer droplet can increase or decrease with the rise in channel confinement depending on the electric properties (conductivity and permittivity) of the system. The present study further takes into account the effect of eccentricity of the inner droplet. Depending on the relative magnitude of the permittivity and conductivity of the system, the inner droplet, if eccentrically located, may exhibit a to and fro or a simple translational motion. It is seen that increase in the channel confinement results in a translational motion of the inner droplet thus rendering its motion independent of any electrical properties. Since the compound droplet model approximately mimics the structure of a cell, the current investigation is expected to provide a significant impact towards predicting the effect of an externally imposed electrical field on the dynamics of a cell in any fluidic confinement and hence has the potential towards widespread applications in the field of medical diagnostics.

physics.flu-dyn↗

arXiv2018

Hidden Fluid Mechanics: A Navier-Stokes Informed Deep Learning Framework for Assimilating Flow Visualization Data

We present hidden fluid mechanics (HFM), a physics informed deep learning framework capable of encoding an important class of physical laws governing fluid motions, namely the Navier-Stokes equations. In particular, we seek to leverage the underlying conservation laws (i.e., for mass, momentum, and energy) to infer hidden quantities of interest such as velocity and pressure fields merely from spatio-temporal visualizations of a passive scaler (e.g., dye or smoke), transported in arbitrarily complex domains (e.g., in human arteries or brain aneurysms). Our approach towards solving the aforementioned data assimilation problem is unique as we design an algorithm that is agnostic to the geometry or the initial and boundary conditions. This makes HFM highly flexible in choosing the spatio-temporal domain of interest for data acquisition as well as subsequent training and predictions. Consequently, the predictions made by HFM are among those cases where a pure machine learning strategy or a mere scientific computing approach simply cannot reproduce. The proposed algorithm achieves accurate predictions of the pressure and velocity fields in both two and three dimensional flows for several benchmark problems motivated by real-world applications. Our results demonstrate that this relatively simple methodology can be used in physical and biomedical problems to extract valuable quantitative information (e.g., lift and drag forces or wall shear stresses in arteries) for which direct measurements may not be possible.

cs.CE↗

arXiv2019

The winner takes all: Volume-scavenging populations of networked droplets

In this work we present and analyze a fluid-mechanical model of competition (scavenging) amongst $N$ liquid droplets (individual competitors). The eventual outcome of this competition depends sensitively on the average resource (volume) per individual $\overline{V}$. For abundant resource, $\overline{V}>1$, there is one winner only and that winner eventually scavenges all or most of the resource. In the socio-economic realm this is is known as the "winner-take-all" outcome: A disproportionately large reward falls to one or a few winners, even though other competitors start out with comparable (or even slightly more) resource and perform only marginally worse. The losing competitors are not rewarded. For less than abundant resource, $\overline{V}<1$, an outcome with resource that is evenly partitioned amongst the $N$ droplets becomes possible. This is the "all-share-evenly" or egalitarian outcome. For sufficiently scarce resource the egalitarian outcome is the only one that can occur. In addition to predicting what kind and how many winners, our analysis shows that once an individual's resource (droplet volume) falls below a fixed threshold, that individual can neither recover nor emerge as winner. This is the "once down-and-out, always down-and-out" outcome. Selected simulations suggest that the winner depends sensitively on population size and the "trading friction" or inefficiency of resource exchange between individuals (liquid rheology). Of all feasible rest states (equilibria), only certain ones are reachable (stable equilibria). Friction turns out to strongly influence the time to reach an end state (stable equilibrium), in surprising ways. Besides the end states, our analysis reveals an array of rest states, ordered in hierarchies of more versus less costly (energetic) outcomes.

physics.flu-dyn↗

arXiv2018

Transport equation for the drift velocity in predicting the filtered Eulerian drag force: a theoretical development

The drift velocity has been proven to have significant relevance to the filtered Eulerian drag force by numerous correlative analyses of fully resolved simulations. It is a sub-grid quantity defined as the difference between the filtered gas velocity seen by the particle phase and the resolved filtered gas velocity. In literature, it is shown that various algebraic models for the drift velocity fail to give entirely satisfactory prediction of the filtered drag force. Unlike previous works, we theoretically derived the transport equation for the drift velocity from the standard two-fluid model (TFM) equations without any additional assumptions. The new approach, though requires additional closures for the new unresolved terms, is believed to have the potential to improve the precision of the estimation of this sub-grid quantity and hence give better prediction of the filtered drag force for gas-solid fluidization problems.

physics.flu-dyn↗

arXiv2018

Effect of Cavitating-bubble Generators on the Dynamics of Unsteady Cloud Cavitation

The present paper is devoted to the 3D numerical study of unsteady cloud cavitation around the CAV2003 benchmark hydrofoil using a passive cavitation controller method called cavitation-bubble generator (CGs). We investigate this passive controller on the hydrofoil surface to affect the whole processes of vaporization, bubble generation and bubble implosion. Firstly we simulate the unsteady cavitating flow around the hydrofoil without CGs using a Partially- averaged Navier Stokes (PANS) method. The turbulence approach is coupled with a mass transfer model which implements to an open source finite-volume package. Then we tested different sizes and angles of CGs on the hydrofoil surface. The results of an appropriate design of the CGs shows a significant decrease of the maximum length of the attached cavity and a large decrease of wall-pressure fluctuation intensity on the hydrofoil surface.

physics.flu-dyn↗

arXiv2018

Pseudopotential multiple-relaxation-time lattice Boltzmann simulation of vapor condensation on vertical subcooled walls

Saturated vapor condensation on the homogeneous and heterogeneous sub-cooled wall under gravity was numerically simulated by the improved pseudo-potential phase-change multiple-relaxation-time lattice Boltzmann (LB) method. Firstly, the phase-change LB method coupling finite different method to solve the energy equation was verified by the D-2 law of the droplets evaporation, which improve the model could precisely realize the numerical simulation of phase change.

physics.flu-dyn↗

arXiv2018

Entropy-stable hybridized discontinuous Galerkin methods for the compressible Euler and Navier-Stokes equations

In the spirit of making high-order discontinuous Galerkin (DG) methods more competitive, researchers have developed the hybridized DG methods, a class of discontinuous Galerkin methods that generalizes the Hybridizable DG (HDG), the Embedded DG (EDG) and the Interior Embedded DG (IEDG) methods. These methods are amenable to hybridization (static condensation) and thus to more computationally efficient implementations. Like other high-order DG methods, however, they may suffer from numerical stability issues in under-resolved fluid flow simulations. In this spirit, we introduce the hybridized DG methods for the compressible Euler and Navier-Stokes equations in entropy variables. Under a suitable choice of the stabilization matrix, the scheme can be shown to be entropy stable and satisfy the Second Law of Thermodynamics in an integral sense. The performance and robustness of the proposed family of schemes are illustrated through a series of steady and unsteady flow problems in subsonic, transonic, and supersonic regimes. The hybridized DG methods in entropy variables show the optimal accuracy order given by the polynomial approximation space, and are significantly superior to their counterparts in conservation variables in terms of stability and robustness, particularly for under-resolved and shock flows.

physics.comp-ph↗

arXiv2018

Stochastic subgrid-scale parameterization for one-dimensional shallow water dynamics using stochastic mode reduction

We address the question of parameterizing the subgrid scales in simulations of geophysical flows by applying stochastic mode reduction to the one-dimensional stochastically forced shallow water equations. The problem is formulated in physical space by defining resolved variables as local spatial averages over finite-volume cells and unresolved variables as corresponding residuals. Based on the assumption of a time-scale separation between the slow spatial averages and the fast residuals, the stochastic mode reduction procedure is used to obtain a low-resolution model for the spatial averages alone with local stochastic subgrid-scale parameterization coupling each resolved variable only to a few neighboring cells. The closure improves the results of the low-resolution model and outperforms two purely empirical stochastic parameterizations. It is shown that the largest benefit is in the representation of the energy spectrum. By adjusting only a single coefficient (the strength of the noise) we observe that there is a potential for improving the performance of the parameterization, if additional tuning of the coefficients is performed. In addition, the scale-awareness of the parameterizations is studied.

physics.flu-dyn↗

arXiv2018

Particle relabelling symmetries and Noether's theorem for vertical slice models

We consider the variational formulation for vertical slice models introduced in Cotter and Holm (Proc Roy Soc, 2013). These models have a Kelvin circulation theorem that holds on all materially-transported closed loops, not just those loops on isosurfaces of potential temperature. Potential vorticity conservation can be derived directly from this circulation theorem. In this paper, we show that this property is due to these models having a relabelling symmetry for every single diffeomorphism of the vertical slice that preserves the density, not just those diffeomorphisms that preserve the potential temperature. This is developed using the methodology of Cotter and Holm (Foundations of Computational Mathematics, 2012).

math-ph↗