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arXiv2014

Mathematical Modeling on Open Limestone Channel

Acid mine drainage (AMD) is the outflow of acidic water from metal mines or coal mines. When exposed to air and water, metal sulfides from the deposits of the mines are oxidized and produce acid, metal ions and sulfate, which lower the pH value of the water. An open limestone channel (OLC) is a passive and low cost way to neutralize AMD. The dissolution of calcium into the water increases the pH value of the solution. A differential equation model is numerically solved to predict the variation of concentration of each species in the OLC solution. The diffusion of Calcium due to iron precipitates is modeled by a linear equation. The results give the variation of pH value and the concentration of Calcium.

physics.chem-ph↗

arXiv2014

An Opto-Electric Micropump for Saline Fluids

A novel method to pump fluid in lab on chip devices with velocities up to tens of micrometer per second is introduced. A focused laser beam locally heats up an electrolyte. A net charge tends to accumulate in the heat-absorbing area, due to unequal tendencies of positive and negative ions to move in the presence of the temperature gradient. An external electric field then exerts a net force on the accumulated charge and consequently on water. This causes flow of water, with velocities up to tens of micrometer per second, for a simple NaCl+water solution. The method lets us change direction and amount of fluid pumping, simply by replacing the focal area.

cond-mat.soft↗

arXiv2014

Energetics of a fluid under the Boussinesq approximation

This paper presents a theory describing the energy budget of a fluid under the Boussinesq approximation: the theory is developed in a manner consistent with the conservation law of mass. It shows that no potential energy is available under the Boussinesq approximation, and also reveals that the work done by the buoyancy force due to changes in temperature corresponds to the conversion between kinetic and internal energy. This energy conversion, however, makes only an ignorable contribution to the distribution of temperature under the approximation. The Boussinesq approximation is, in physical oceanography, extended so that the motion of seawater can be studied. This paper considers this extended approximation as well. Under the extended approximation, the work done by the buoyancy force due to changes in salinity corresponds to the conversion between kinetic and potential energy. It also turns out that the conservation law of mass does not allow the condition $\nabla\cdot\boldsymbol{u}=0$ on the fluid velocity $\boldsymbol{u}$ to be imposed under the extended approximation; the condition to be imposed instead is presented.

physics.flu-dyn↗

arXiv2014

Short- and Long- Time Transport Structures in a Three Dimensional Time Dependent Flow

Lagrangian transport structures for three-dimensional and time-dependent fluid flows are of great interest in numerous applications, particularly for geophysical or oceanic flows. In such flows, chaotic transport and mixing can play important environmental and ecological roles, for examples in pollution spills or plankton migration. In such flows, where simulations or observations are typically available only over a short time, understanding the difference between short-time and long-time transport structures is critical. In this paper, we use a set of classical (i.e. Poincaré section, Lyapunov exponent) and alternative (i.e. finite time Lyapunov exponent, Lagrangian coherent structures) tools from dynamical systems theory that analyze chaotic transport both qualitatively and quantitatively. With this set of tools we are able to reveal, identify and highlight differences between short- and long-time transport structures inside a flow composed of a primary horizontal contra-rotating vortex chain, small lateral oscillations and a weak Ekman pumping. The difference is mainly the existence of regular or extremely slowly developing chaotic regions that are only present at short time.

physics.flu-dyn↗

arXiv2014

Quantfying rich patterns in agglomeration of floating beads

Macroscopic spherical particles spontaneously form rich patterns on a standing Faraday wave. These patterns are found to follow a very systematic trend depending on the floater concentration $ϕ$: The same floaters that accumulate at amplitude maxima (antinodes) of the wave at low $ϕ$, surprisingly move towards the nodal lines when $ϕ$ is beyond a certain value. In more detail, circular irregularly packed antinode clusters at low $ϕ$ give way to loosely packed filamentary structures at intermediate $ϕ$, and are then followed by densely packed grid-shaped node clusters at high $ϕ$. Here, we successfully characterize the morphology of these rich patterns using a metric analysis, i.e., the Minkowski functionals. We modify the Minkowski functionals such that we are able to measure the physical quantities of the clusters such as area, perimeter, and aspect ratio.

physics.flu-dyn↗

arXiv2014

Relative-Periodic Elastic Collisions of Water Waves

We compute time-periodic and relative-periodic solutions of the free-surface Euler equations that take the form of overtaking collisions of unidirectional solitary waves of different amplitude on a periodic domain. As a starting guess, we superpose two Stokes waves offset by half the spatial period. Using an overdetermined shooting method, the background radiation generated by collisions of the Stokes waves is tuned to be identical before and after each collision. In some cases, the radiation is effectively eliminated in this procedure, yielding smooth soliton-like solutions that interact elastically forever. We find examples in which the larger wave subsumes the smaller wave each time they collide, and others in which the trailing wave bumps into the leading wave, transferring energy without fully merging. Similarities notwithstanding, these solutions are found quantitatively to lie outside of the Korteweg-de Vries regime. We conclude that quasi-periodic elastic collisions are not unique to integrable model water wave equations when the domain is periodic.

physics.flu-dyn↗

arXiv2014

Experimental and numerical determination of mechanical properties of polygonal wood particles and their flow analysis in silos

Responding to a lack in the literature, mechanical properties of polygonal wood particles are determined for use in a discrete element model (DEM) for flow analysis in silos, and some methods are proposed for determining such parameters. The parameters arrived at here have also formed part of the input to the SPOLY software, developed in-house to compute the DEM model with spheropolyhedron elements. The model is validated using a 2D physical model, where prismatic particles with polygonal cross sections are placed inside a silo with variable aperture and hopper angle. Validation includes comparison of flow-rates computed by SPOLY, displacement profiles, and clogging thresholds with experimental results. The good agreement that emerges will encourage future use of miniature triaxial tests, grain-surface profilometry, inclined slope tests, and numerical analysis of the intragranular stresses - toward a direct construction of the contact-deformation relations required in realistic DEM modelling of particle flow with angular-shaped particles.

cond-mat.soft↗

arXiv2014

Time-resolved particle image velocimetry measurements with wall shear stress and uncertainty quantification for the FDA benchmark nozzle model

We present validation of benchmark experimental data for computational fluid dynamics (CFD) analyses of medical devices using advanced Particle Image Velocimetry (PIV) processing and post-processing techniques. This work is an extension of a previous FDA-sponsored multi-laboratory study, which used a medical device mimicking geometry referred to as the FDA benchmark nozzle model. Time-resolved PIV analysis was performed in five overlapping regions of the model for Reynolds numbers in the nozzle throat of 500, 2,000, 5,000, and 8,000. Images included a two-fold increase in spatial resolution in comparison to the previous study. Data was processed using ensemble correlation, dynamic range enhancement, and phase correlations to increase signal-to-noise ratios and measurement accuracy, and to resolve flow regions with large velocity ranges and gradients, which is typical of many blood-contacting medical devices. Parameters relevant to device safety, including shear stress at the wall and in bulk flow, were computed using radial basis functions (RBF) to improve accuracy. In-field spatially resolved pressure distributions, Reynolds stresses and energy dissipation rates were computed from PIV measurements. Velocity measurement uncertainty was estimated directly from the PIV correlation plane, and uncertainty analysis for wall shear stress at each measurement location was performed using a Monte Carlo model. (truncated abstract)

physics.flu-dyn↗

arXiv2014

Extending a serial 3D two-phase CFD code to parallel execution over MPI by using the PETSc library for domain decomposition

To leverage the last two decades' transition in High-Performance Computing (HPC) towards clusters of compute nodes bound together with fast interconnects, a modern scalable CFD code must be able to efficiently distribute work amongst several nodes using the Message Passing Interface (MPI). MPI can enable very large simulations running on very large clusters, but it is necessary that the bulk of the CFD code be written with MPI in mind, an obstacle to parallelizing an existing serial code. In this work we present the results of extending an existing two-phase 3D Navier-Stokes solver, which was completely serial, to a parallel execution model using MPI. The 3D Navier-Stokes equations for two immiscible incompressible fluids are solved by the continuum surface force method, while the location of the interface is determined by the level-set method. We employ the Portable Extensible Toolkit for Scientific Computing (PETSc) for domain decomposition (DD) in a framework where only a fraction of the code needs to be altered. We study the strong and weak scaling of the resulting code. Cases are studied that are relevant to the fundamental understanding of oil/water separation in electrocoalescers.

physics.comp-ph↗

arXiv2014

Control of a Backward-Facing Step flow through vortex pairing and phase locking

Many experimental and numerical studies report a large reduction of the recirculation bubble in Backward-Facing Step flows or airfoils in stall situation when excited at the natural shedding frequency $f_0$. Through a simple experiment using Dielectric Barrier Discharge actuator, we find a different result. For a given Reynolds number, the frequency of the perturbation is varied for a fixed duty-cycle dc = 27%. Through phase-averaging of Particle Image Velocimetry measurements, we show that the actuation creates a forced vortex which interacts with the natural shedding with a different phase velocity than the unforced one. The largest reduction of the recirculation bubble (-35%) is obtained in a very narrow frequency range around $0.73 f_0$ where early vortex pairing occurs between forced and unforced vortices. Phase averaging shows that in this case, the actuation clearly forces the vortex pairing in the shear layer. On the contrary, when the forcing frequency is higher, the shear layer behaves like an amplifier synchronized on the forced frequency, leading to a constant 10% reduction of the recirculation bubble.

physics.flu-dyn↗

arXiv2014

A Statistical Model of Pressure Drop Increase with Deposition in Granular Filters

As deposits accumulate in a granular filter, pressure drop across the filter bed required to maintain a constant fluid flow rate may increase. Two pressure drop increase patterns had been observed. In slow sand filters pressure drop remains unchanged for a certain period of time then increases exponentially with the volume of filtrate; in granular aerosol filters pressure drop increases linearly with the amount of deposits from the beginning of the filtration process. New concepts of homogeneous and heterogeneous depositions were introduced in this paper. A statistical model based on these new concepts was developed. This non-linear model was able to reproduce both observed pressure drop increase patterns, including the linear one. Excellent agreements between the present model and experimental measurements were obtained. It was concluded that the two pressure drop increase patterns were indeed caused by different deposit distributions rather than different pressure drop increase mechanisms.

cond-mat.soft↗

arXiv2014

An accurate and efficient numerical framework for adaptive numerical weather prediction

We present an accurate and efficient discretization approach for the adaptive discretization of typical model equations employed in numerical weather prediction. A semi-Lagrangian approach is combined with the TR-BDF2 semi-implicit time discretization method and with a spatial discretization based on adaptive discontinuous finite elements. The resulting method has full second order accuracy in time and can employ polynomial bases of arbitrarily high degree in space, is unconditionally stable and can effectively adapt the number of degrees of freedom employed in each element, in order to balance accuracy and computational cost. The p-adaptivity approach employed does not require remeshing, therefore it is especially suitable for applications, such as numerical weather prediction, in which a large number of physical quantities are associated with a given mesh. Furthermore, although the proposed method can be implemented on arbitrary unstructured and nonconforming meshes, even its application on simple Cartesian meshes in spherical coordinates can cure effectively the pole problem by reducing the polynomial degree used in the polar elements. Numerical simulations of classical benchmarks for the shallow water and for the fully compressible Euler equations validate the method and demonstrate its capability to achieve accurate results also at large Courant numbers, with time steps up to 100 times larger than those of typical explicit discretizations of the same problems, while reducing the computational cost thanks to the adaptivity algorithm.

math.NA↗

arXiv2014

Filamentary vortex in a swirling turbulent flow under strong stretching

Energy dissipation and pressure fluctuations are features inherent to turbulent fluid motion, and the internal origin of spatial and temporal temperature fluctuations. By measuring local velocity, pressure or temperature, it is possible to detect the presence of coherent structures ---like concentrated vortices--- and quantify their intensity. Here we report measurements of speed and temperature in a filamentary vortex lying in a strongly stretched turbulent airflow. The largest core temperature drop measured in our experiment was $ΔT = 9$ K, while the fastest measured air speed was $v_{max} = 200$ m/s, which corresponds to a Mach number $M_{max} = 0.59$. At $M \approx 0.1$ temperature drops are on the order of $0.5$ K. These results are consistent with the model for compressible vortices by Aboelkassem and Vatistas [J. Fluids Eng. 129, 1073 (2007)].

physics.flu-dyn↗

arXiv2014

Multiscale modelling couples patches of two-layer thin fluid flow

The multiscale gap-tooth scheme uses a given microscale simulator of complicated physical processes to enable macroscale simulations by computing only only small sparse patches. This article develops the gap-tooth scheme to the case of nonlinear microscale simulations of thin fluid flow. The microscale simulator is derived by artificially assuming the fluid film flow having two artificial layers but no distinguishing physical feature. Centre manifold theory assures that there exists a slow manifold in the two-layer fluid film flow. Eigenvalue analysis confirms the stability of the microscale simulator. This article uses the gap-tooth scheme to simulate the two-layer fluid film flow. Coupling conditions are developed by approximating the values at the edges of patches by neighbouring macroscale values. Numerical eigenvalue analysis suggests that the gap-tooth scheme with the developed two-layer microscale simulator empowers feasible computation of large scale simulations of fluid film flows. We also implement numerical simulations of the fluid film flow by the gap-tooth scheme. Comparison between a gap-tooth simulation and a microscale simulation over the whole domain demonstrates that the gap-tooth scheme feasibly computes fluid film flow dynamics with computational savings.

math.DS↗

arXiv2014

Hysteresis and Lubrication in Shear Thickening of Cornstarch Suspensions

Aqueous and brine suspensions of corn starch show striking discontinuous shear thickening. We have found that a suspension shear-thickened throughout may remain in the jammed thickened state as the strain rate is reduced, but an unjamming front may propagate from any unjammed regions. Transient shear thickening is observed at strain rates below the thickening threshold, and above it the stress fluctuates. The jammed shear-thickened state may persist to low strain rates, with stresses resembling sliding friction and effective viscosity inversely proportional to the strain rate. At the thickening threshold fluid pressure depins the suspension's contact lines on solid boundaries so that it slides, shears, dilates and jams. In oil suspensions lubrication and complete wetting of confining surfaces eliminate contact line forces and prevent jamming and shear thickening, as does addition of immiscible liquid surfactant to brine suspensions. Starch suspensions in glycerin-water solutions, viscous but incompletely wetting, have intermediate properties.

cond-mat.soft↗

arXiv2014

Large Drag Reduction over Superhydrophobic Riblets

Riblets and superhydrophobic surfaces are two demonstrated passive drag reduction techniques. We describe a method to fabricate surfaces that combine both of these techniques in order to increase drag reduction properties. Samples have been tested with a cone-and-plate rheometer system, and have demonstrated significant drag reduction even in the transitional-turbulent regime. Direct Numerical Simulations have been performed in order to estimate the equivalent slip length at higher rotational speed. The sample with 100~$μ$m deep grooves has been performing very well, showing drag reduction varying from 15 to 20 $\%$ over the whole range of flow conditions tested, and its slip length was estimated to be over 100 $μ$m.

physics.flu-dyn↗

arXiv2014

Effect of Spatial Heterogeneity on Near-Limit Propagation of a Stable Detonation

The effect of introducing a spatial heterogeneity into an explosive medium is studied computationally by examining the detonation velocity near the limit to propagation in a thin explosive layer. The explosive system studied is an ideal gas with a single exothermic reaction governed by a pressure-dependent reaction rate ($p^n$) with a pressure exponent of $n = 3$. A pressure-dependent reaction rate, rather than the exponential dependence of reaction on temperature of Arrhenius kinetics, is used so that the detonation wave is stable in the homogeneous case and can be modelled with simple, analytical techniques, and thus the effect of introducing heterogeneity can be clearly identified. The two-dimensional slab of explosive is bounded by a layer of inert gas with the same thermodynamic properties as the explosive. The heterogeneity is introduced into the explosive via a large-amplitude, two-dimensional sinusoidal ripple in density in the initialization of the simulation, while maintaining a constant pressure. The computational simulations are initialized with a ZND solution for the ideal CJ detonation, and the detonation is allowed to propagate into the explosive layer. The simulations show that the detonation in the heterogeneous media exhibits a cellular-like structure of complex shock interactions. The detonation is able to propagate into a significantly thinner layer of explosive and can exhibit a greater velocity than the corresponding homogeneous case. A parametric study of varying the wavelength of the sinusoid shows the existence of an optimal size of heterogeneity at which the favorable effect is the greatest corresponding to a wavelength that is approximately 10 to 50 times the half reaction zone length of the ideal CJ detonation. As the wavelength is decreased to the size of the reaction zone length, the behavior reverts back to the homogeneous case.

physics.flu-dyn↗

arXiv2014

Turbulent heat transfer in a channel flow at transitional Reynolds numbers

Direct numerical simulation of a turbulent channel flow with heat transfer was performed at very low Reynolds numbers. Two different thermal boundary conditions were studied, and temperature was considered as a passive scalar. The computations were carried out with huge computational boxes (up to 327.7 x 2 x 128 in the streamwise, wall-normal, and spanwise directions, respectively). The emphases of this paper are to investigate the large-scale structure (puff) in the intermittent-turbulent flow including the scalar fields and to provide the values of the transitional and critical Reynolds numbers, below which the turbulent flow becomes intermittent and laminar, respectively. The statistics, such as the skin friction and the Stanton number, were also examined: they suggest that the puff should be effective in sustaining turbulence and in heat transfer enhancement.

physics.flu-dyn↗