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arXiv2018

Electrokinetic Current Driven by a Viscosity Gradient

Gradients of voltage, pressure, temperature, and salinity can transport objects in micro- and nanofluidic systems by well known mechanisms. Here we report the discovery of a transport effect driven by viscosity gradients, which cause an ionic current to flow inside a glass nanofluidic channel. Measurements of the current are well described by a simple model wherein counterions in the electric double layers near the surfaces drift in the direction of decreasing viscosity with a drift speed equal to the gradient of the ions' local diffusivity. Drift in a viscosity gradient is a consequence of multiplicative (state-dependent) noise, which results from a particle's thermal fluctuations depending on its position. This surprisingly large effect, measured in a highly controlled nanofluidic environment, reveals fundamental behavior that is relevant to a broad range of systems.

physics.flu-dyn↗

arXiv2018

Flapping-pattern change in small and very small insects

Medium and large insects in normal hovering have horizontal, planar up- and downstrokes1-4. The lift of the two half-strokes, generated by the leading-edge vortex, provides the weight-supporting vertical force. But for small insects (wing length R less than about 4 mm and Reynolds number Re very low, about 80 to 10), because of the large effect of air viscosity (as Re becomes very low, moving in air is like in oil), sufficient vertical force could not be produced if using the above wing kinematics. Small insects must use different flapping mode. Here, through analyzing flight data from our recent studies on a relatively-large small insect (fruitfly: R=3 mm, Re=80) and a very small insect (wasp: R=0.5 mm, Re=10), we put forward a hypothesis on how the flapping pattern will change: as insect-size or Re decreasing, a deeper and deeper U-shape upstroke will be used to overcome the viscous effect. And we test this hypothesis by measuring the wing kinematics for species of different sizes to obtain data for Re ranging from 80 to 10 and by computing the aerodynamic forces. The data and computation support our hypothesis: the planar upstroke changes to U-shape upstroke which becomes deeper as size or Re becomes smaller; for relatively-large small insects, the U-shape upstroke produces a larger vertical force than a planar upstroke by having a larger wing velocity, and for very small insects, the deep U-shape upstroke produces a large transient drag that points almost upwards by fast downward acceleration of the wing, providing the required vertical force.

physics.bio-ph↗

arXiv2018

Bursting and reformation cycle of the laminar separation bubble over a NACA-0012 aerofoil: The dynamics of the flow-field

Detailed flow dissection using Dynamic Mode Decomposition (DMD) and Proper Orthogonal Decomposition (POD) is carried out to investigate the dynamics of the flow-field around a NACA-0012 aerofoil at a Reynolds number of $5\times 10^4$, Mach number of $0.4$, and at various angles of attack around the onset of stall. Three distinct dominant flow modes are identified by the DMD and the POD: 1) a globally oscillating flow mode at a low-frequency (LFO mode 1); 2) a locally oscillating flow mode on the suction surface of the aerofoil at a low-frequency (LFO mode 2); and 3) a locally oscillating flow mode along the wake of the aerofoil at a high-frequency (HFO mode). The LFO mode 1 features the globally oscillating-flow around the aerofoil, the oscillating-pressure along the aerofoil chord, and the process that creates and sustains the triad of vortices. The LFO mode 2 features the expansion and advection of the upstream vortex (UV) of the TCV. The HFO mode originates at the aerofoil leading-edge and features the oscillating mode along the aerofoil wake. The HFO mode exists at all of the investigated angles of attack and causes a global oscillation in the flow-field. The global flow oscillation around the aerofoil interacts with the laminar portion of the separated shear layer in the vicinity of the leading-edge and triggers an inviscid absolute instability that creates and sustains the TCV. When the UV of the TCV expands, it advects downstream and energies the HFO mode. The LFO mode 1, the LFO mode 2, and the HFO mode mutually strengthen each other until the LFO mode 1 and 2 overtake the HFO mode at the onset of stall. At the angles of attack $9.7^{\circ} \leq α\leq 10.0^{\circ}$ the low-frequency flow oscillation (LFO) phenomenon is fully developed. At higher angles of attack, the HFO mode overtakes the LFO mode 2, and the aerofoil undergoes a full stall.

physics.flu-dyn↗

arXiv2019

A Hybrid Data-driven Deep Learning Technique for Fluid-Structure Interaction

This paper is concerned with the development of a hybrid data-driven technique for unsteady fluid-structure interaction systems. The proposed data-driven technique combines the deep learning framework with a projection-based low-order modeling. While the deep learning provides low-dimensional approximations from datasets arising from black-box solvers, the projection-based model constructs the low-dimensional approximations by projecting the original high-dimensional model onto a low-dimensional subspace. Of particular interest of this paper is to predict the long time series of unsteady flow fields of a freely vibrating bluff-body subjected to wake-body synchronization. We consider convolutional neural networks (CNN) for the learning dynamics of wake-body interaction, which assemble layers of linear convolutions with nonlinear activations to automatically extract the low-dimensional flow features. Using the high-fidelity time series data from the stabilized finite element Navier-Stokes solver, we first project the dataset to a low-dimensional subspace by proper orthogonal decomposition (POD) technique. The time-dependent coefficients of the POD subspace are mapped to the flow field via a CNN with nonlinear rectification, and the CNN is iteratively trained using the stochastic gradient descent method to predict the POD time coefficient when a new flow field is fed to it. The time-averaged flow field, the POD basis vectors, and the trained CNN are used to predict the long time series of the flow fields and the flow predictions are quantitatively assessed with the full-order (high-dimensional) simulation data. The proposed POD-CNN model based on the data-driven approximation has a remarkable accuracy in the entire fluid domain including the highly nonlinear near wake region behind a freely vibrating bluff body.

physics.comp-ph↗

arXiv2018

Turbulucid: A Python Package for Post-Processing of Fluid Flow Simulations

A Python package for post-processing of plane two-dimensional data from computational fluid dynamics simulations is presented. The package, called turbulucid, provides means for scripted, reproducible analysis of large simulation campaigns and includes routines for both data extraction and visualization. For the former, the Visualization Toolkit (VTK) is used, allowing for post-processing of simulations performed on unstructured meshes. For visualization, several matplotlib-based functions for creating highly customizable, publication-quality plots are provided. To demonstrate turbulucid's functionality it is here applied to post-processing a simulation of a flow over a backward-facing step. The implementation and architecture of the package are also discussed, as well as its reuse potential.

cs.CE↗

arXiv2018

The deformation of a flexible fiber settling in a quiescent viscous fluid

The equilibrium state of a flexible fiber settling in a viscous fluid is examined using a combination of macroscopic experiments, numerical simulations and scaling arguments. We identify three regimes having different signatures on this equilibrium configuration of the elastic filament: weak and large deformation regimes wherein the drag is proportional to the settling velocity as expected in Stokes flow and an intermediate elastic reconfiguration regime where the filament deforms to adopt a shape with a smaller drag which is no longer linearly proportional to the velocity.

physics.flu-dyn↗

arXiv2018

A mass entrainment-based model for separating/reattaching flows

Recent studies have shown that entrainment effectively describes the behaviour of natural and forced separating/reattaching flows developing behind bluff bodies, potentially paving the way to new, scalable separation control strategies. In this perspective, we propose a new interpretative framework for separated flows, based on mass entrainment. The cornerstone of the approach is an original model of the mean flow, representing it as a stationary vortex scaling with the mean recirculation length. We test our model on a set of mean separated topologies, obtained by forcing the flow over a descending ramp with a rack of synthetic jets. Our results show that both the circulation of the vortex and its characteristic size scale simply with the intensity of the backflow (i.e. the amount of mass going through the recirculation region). This suggests that the vortex model captures the essential functioning of mean mass entrainment, and that it could be used to model and/or predict the mean properties of separated flows. In addition, we use the vortex model to show that the backflow (i.e. an integral quantity) can be estimated from a single wall-pressure measurement (i.e. a pointwise quantity). Since the backflow also appears to be anticorrelated to the characteristic velocity of the synthetic jets, this finding suggests that industrially deployable, closed-loop control systems based on mass entrainment might be within reach.

physics.flu-dyn↗

arXiv2018

Dean flow and vortex shedding in a three-dimensional 180$^\circ$ sharp bend

We present a detailed analysis of the flow in a 180 sharp bend of square cross-section. Besides numerous applications where this generic configuration is found, its main fundamental interest resides in the co-existence of a recirculation bubble in the outlet and a pair of Dean vortices driven from within the turning part of the bend, and how their interaction may drive the flow dynamics. A critical point analysis first shows that the complex flow topology that results from this particular configuration can be reduced to three pairs of critical points in the symmetry plane of the bend (with a focus and a half-saddle each). These pairs respectively generate the first recirculation bubble, the pair of Dean vortex tubes and a third pair of vortex tubes located in the upper corner of the bend, akin to the Dean vortices but of much lower intensity and impact on the rest of the flow. The Dean flow by contrast drives a strong vertical jet that splits the recirculation bubble into two symmetric lobes. Unsteadiness sets in at $Re\lesssim800$ through a supercritical bifurcation, as these lobes start oscillating antisymmetrically. These initially periodic oscillations grow in amplitude until the lobes break away from the main recirculation. The system then settles into a second periodic state where streamwise vortices driven by the Dean flow are alternatively formed and shed on the left and right part of the outlet. This novel mechanism of periodic vortex shedding results from the subtle interaction between the recirculation bubble in the outlet and the pair of Dean vortices generated in the turning part, and in this sense, they are expected to be a unique feature of the 180$^o$ bend with sufficiently close side walls.

physics.flu-dyn↗

arXiv2018

SPH Consistent With Explicit LES

The aim of this paper is to introduce a consistent velocity smoothing method for smoothed particle hydrodynamics (SPH). First the locally averaged Navier-Stokes equations are derived in a mathematically rigorous way to demonstrate the "missing" turbulent stress in standard SPH formulations. It is then shown that with a proper choice of velocity smoothing, SPH and large eddy simulation (LES) equivalently solve the same set of filtered equations that require closure approximations. The only difference between SPH and LES, as demonstrated in this paper is the representation of governing equations; for the former the equations are in integro-differential form whereas for the latter they are in differential form. One direct consequence of this equivalence between SPH and LES is that turbulence modeling techniques originally developed for LES can easily be adopted into this version of SPH. Our representation of the sub-grid stress tensor in integral form will provide insight into alternative approaches for dealing with turbulence modeling. Although the use of the Smagorinsky model is the common practice for turbulence modeling in LES, it will be shown that for SPH the most natural choice is to use approximate deconvolution methods. The other particularly fundamental consequence of our choice of velocity smoothing is that the resulting filtered equations are nonconservative in nature and a correct Lagrangian cannot be easily constructed.

physics.flu-dyn↗

arXiv2018

Unsmoothed Particle Hydrodynamics

The aim of this paper is to introduce a new computational fluid dynamics method to be called unsmoothed particle hydrodynamics SPH$-i$ which makes few assumptions and makes no assumption beyond the Navier-Stokes equations. The most attractive feature when compared with standard smoothed particle hydrodynamics (SPH) is that no explicit turbulence modeling is required. Furthermore, despite being a high order model, it retains the same, simple structure as standard SPH. In this sense SPH$-i$ is a coarse-grained direct numerical simulation approach. In SPH, due the scale-dependence resulting from the convolution operator, all modes below the kernel cut-off length, are filtered out leading to loss of information. However, we conjecture that the SPH field, theoretically, still contains enough information so that the SPH$-i$ field is a restored form of the original underlying continuum field. Since two filters are required, a rigorous technique for constructing compatible convolution and deconvolution filters is presented. The SPH$-i$ model is relatively easy to implement.

physics.flu-dyn↗

arXiv2018

Measurement of interfacial wave dynamics in orbitally shaken cylindrical containers using ultrasound pulse-echo techniques

We present a novel experiment on interfacial wave dynamics in orbitally shaken cylindrical vessels containing two- and three fluid layers. The experiment was designed as a hydrodynamical model for both alu- minum reduction cells and liquid metal batteries to gain new insights into the rotational wave motion driven by the metal pad roll instability. Different options are presented to realize stable and measurable multi-layer stratifications. We introduce a new acoustic measure- ment procedure allowing to reconstruct wave ampli- tudes also in opaque liquids by tracking ultrasonic pulse echoes reflected on the interfaces. Measurements of res- onance curves and phase shifts were conducted for vary- ing interface positions. A strong influence of the top and bottom walls were observed, considerably reducing wave amplitudes and eigenfrequencies, when the inter- face is getting close. Finally, measured resonance curves were successfully compared with an existing forced wave theory that we extended to two-layer interfacial waves. The comparison stresses the importance to carefully control the boundary condition at the contact line.

physics.flu-dyn↗

arXiv2018

A time-space Hausdorff fractal model for non-Fickian transport in porous media

This paper presents a time-space Hausdorff derivative model for depicting solute transport in aquifers or water flow in heterogeneous porous media. In this model, the time and space Hausdorff derivatives are defined on non-Euclidean fractal metrics with power law scaling transform which, respectively, connect the temporal and spatial complexity during transport. The Hausdorff derivative model can be transformed to an advection-dispersion equation with time- and space-dependent dispersion and convection coefficients. This model is a fractal partial differential equation (PDE) defined on a fractal space and differs from the fractional PDE which is derived for non-local transport of particles on a non-fractal Euclidean space. As an example of applications of this model, an explicit solution with a constant diffusion coefficient and flow velocity subject to an instantaneous source is derived and fitted to the breakthrough curves of tritium as a tracer in porous media. These results are compared with those of a scale-dependent dispersion model and a time-scale dependent dispersion model. Overall, it is found that the fractal PDE based on the Hausdorff derivatives better captures the early arrival and heavy tail in the scaled breakthrough curves for variable transport distances. The estimated parameters in the fractal Hausrdorff model represent clear physical mechanisms such as linear relationships between the orders of Hausdorff derivatives and the transport distance. The mathematical formulation is applicable to both solute transport and water flow in porous media.

physics.flu-dyn↗

arXiv2018

Direct numerical simulation of developed compressible flow in square ducts

We carry out direct numerical simulation of compressible square duct flow in the range of bulk Mach numbers M_b = 0.2-3, and up to friction Reynolds number Re_τ = 500. The effects of flow compressibility on the secondary motions are found to be negligible, as the typical Mach number associated with the cross-stream flow is always less than 0.1. As in the incompressible case, we find that the wall law for the mean streamwise velocity applies with good approximation with respect to the nearest wall, upon suitable compressibility transformation. The same conclusion also applies to a passive scalar field, whereas the mean temperature does not exhibit inertial layers because of nonuniformity of the aerodynamic heating. We further find that the same temperature/velocity relation that holds for planar channels is applicable with good approximation for square ducts, and develop a similar relation between temperature and passive scalars.

physics.flu-dyn↗

arXiv2018

Longwave nonlinear theory for chemically active droplet division instability

It has been suggested recently that growth and division of a protocell could be modeled by a chemically active droplet with simple chemical reactions driven by an external fuel supply. This model is called the continuum model. Indeed it's numerical simulation reveals a shape instability which results in droplet division into two smaller droplets of equal size resembling cell division [1]. In this paper, we investigate the reduced version of the continuum model, which is called the effective model. This model is studied both in the linear and nonlinear regime. First, we perform a linear stability analysis for the flat interface, and then we develop a nonlinear theory using the longwave approach. We find that the interface at the leading order is governed by the modified Kuramoto-Sivashinsky equation. Therefore the interface is subject to a logarithmic blow up after a finite time. In addition, an expression for the interface local velocity is obtained.

physics.bio-ph↗

arXiv2018

Enhanced locomotion, effective diffusion, and trapping of undulatory micro-swimmers in heterogeneous environments

Swimming cells and microorganisms must often move though complex fluids that contain an immersed microstructure such as polymer molecules, or filaments. In many important biological processes, such as mammalian reproduction and bacterial infection, the size of the immersed microstructure is comparable to that of the swimming cells. This leads to discrete swimmer-microstructure interactions that alter the swimmer's path and speed. In this paper, we use a combination of detailed simulation and data-driven stochastic models to examine the motion of a planar undulatory swimmer in an environment of spherical obstacles tethered via linear springs to random points in the plane of locomotion. We find that depending on environmental parameters, the interactions with the obstacles can both enhance swimming speeds, as well as prevent the swimmer from moving at all. We also show how the discrete interactions produce translational and angular velocity fluctuations that over time lead to diffusive behaviour primarily due to the coupling of swimming and rotational diffusion. Our results demonstrate that direct swimmer-microstructure interactions can produce changes in swimmer motion that may have important implications to the spreading of cell populations in, or the trapping of harmful pathogens by complex fluids.

physics.flu-dyn↗

arXiv2018

GPU parallelization of a hybrid pseudospectral fluid turbulence framework using CUDA

An existing hybrid MPI-OpenMP scheme is augmented with a CUDA-based fine grain parallelization approach for multidimensional distributed Fourier transforms, in a well-characterized pseudospectral fluid turbulence code. Basics of the hybrid scheme are reviewed, and heuristics provided to show a potential benefit of the CUDA implementation. The method draws heavily on the CUDA runtime library to handle memory management, and on the cuFFT library for computing local FFTs. The manner in which the interfaces are constructed to these libraries, and ISO bindings utilized to facilitate platform portability, are discussed. CUDA streams are implemented to overlap data transfer with cuFFT computation. Testing with a baseline solver demonstrates significant aggregate speed-up over the hybrid MPI-OpenMP solver by offloading to GPUs on an NVLink-based test system. While the batch streamed approach provides little benefit with NVLink, we see a performance gain of 30% when tuned for the optimal number of streams on a PCIe-based system. It is found that strong GPU scaling is ideal, or slightly better than ideal, in all cases. In addition to speed-up measurements for the fiducial solver, we also consider several other solvers with different numbers of transform operations and find that aggregate speed-ups are nearly constant for all solvers.

physics.comp-ph↗

arXiv2018

Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems

Model reduction of high-dimensional dynamical systems alleviates computational burdens faced in various tasks from design optimization to model predictive control. One popular model reduction approach is based on projecting the governing equations onto a subspace spanned by basis functions obtained from the compression of a dataset of solution snapshots. However, this method is intrusive since the projection requires access to the system operators. Further, some systems may require special treatment of nonlinearities to ensure computational efficiency or additional modeling to preserve stability. In this work we propose a deep learning-based strategy for nonlinear model reduction that is inspired by projection-based model reduction where the idea is to identify some optimal low-dimensional representation and evolve it in time. Our approach constructs a modular model consisting of a deep convolutional autoencoder and a modified LSTM network. The deep convolutional autoencoder returns a low-dimensional representation in terms of coordinates on some expressive nonlinear data-supporting manifold. The dynamics on this manifold are then modeled by the modified LSTM network in a computationally efficient manner. An offline unsupervised training strategy that exploits the model modularity is also developed. We demonstrate our model on three illustrative examples each highlighting the model's performance in prediction tasks for fluid systems with large parameter-variations and its stability in long-term prediction.

math.DS↗

arXiv2018

The piston effect induced by mass transfer in a binary fluid mixture near the critical point

Similar to pure fluids, physical properties of a binary fluid mixture also exhibit singularities close to its critical point, especially when it is dilute. The numerical and theoretical results presented in this paper identify that the piston effect, a rapid energy transfer phenomenon, can be induced by boundary mass transfer in a confined near-critical binary fluid mixture. Due to the Dufour effect, both the concentration and temperature variations are responsible for the strong expansion of the boundary layer, which provokes an acoustic wave propagating in the fluid, leading to a gradual increase of the temperature, pressure and density. The detailed analysis implies that such a mixed piston effect can be approximated as a direct superposition of their respective effects in the perspective of energy transformation.

physics.flu-dyn↗