Hydrodynamic Systems Research Articles

Quantum hydrodynamics from large-n supersymmetric gauge theories

We study the connection between periodic finite-difference Intermediate Long Wave hydrodynamical systems and integrable many-body models of Calogero and Ruijsenaars-type. The former describe quantum cohomology and quantum K-theory of the ADHM moduli space of Abelian instantons, while the latter arise in the the instanton counting in four and five dimensional supersymmetric gauge theories with eight supercharges in the presence of defects. Using string theory dualities we provide correspondences between hydrodynamical and many-body integrable systems. In particular, we match the energy spectra on both sides.

Transport Matters: Boosting CO2 Electroreduction in Mixtures of [BMIm][BF4 ]/Water by Enhanced Diffusion.

Room-temperature ionic liquids (RTILs) are promising new electrolytes for efficient carbon dioxide reduction. However, due to their high viscosity, the mass transport of CO2 in RTILs is typically slow, at least one order of magnitude slower than in aqueous systems. One possibility to improve mass transport in RTILs is to decrease their viscosity through dilution with water. Herein, defined amounts of water are added to 1-butyl-3methylimidazolium tetrafluoroborate ([BMIm][BF4 ]), which is a hydrophilic RTIL. Electrochemical measurements on quiescent and hydrodynamic systems both indicate enhanced CO2 electroreduction. This enhancement has its origin in thermodynamic/kinetic effects (the addition of water increases the availability of H+ , which is a reaction partner of CO2 electroreduction) and in an increased rate of transport due to lower viscosity. Electrochemically determined diffusion coefficients for CO2 in [BMIm][BF4 ]/water systems agree well with values determined by NMR spectroscopy.

Asymptotics of stochastic 2D hydrodynamical type systems in unbounded domains

In this paper, we prove a central limit theorem and establish a moderate deviation principle for 2D stochastic hydrodynamical type systems with multiplicative noise in unbounded domains, which covers 2D Navier–Stokes equations, 2D MHD models and the 2D magnetic Bénard problem and also shell models of turbulence. The weak convergence method plays an important role in obtaining the moderate deviation principle.

The Impedance Analyzer: An Open-Source, Web-Based Tool for Sophisticated Interrogation of Experimental EIS Spectra

Electrochemical impedance spectroscopy (EIS) is a powerful technique for partitioning a system’s performance into contributions from individual physicochemical processes via their characteristic frequencies.1 Typically, analysis of experimental EIS spectra aims to extract meaningful information by fitting an equivalent circuit analog composed of ideal circuit elements representing different physicochemical phenomena within the cell. While fitting an equivalent circuit to experimental data is easily accomplished using nonlinear least squares regression, the lumped nature and lack of direct physical interpretation of the resulting parameters can limit the information content of the analysis.2 An alternative approach for extracting meaningful parameters from the data is to directly fit physics-based mathematical models of the electrochemical systems. In fact, many decades of electrochemical modeling research have laid the groundwork for the physics-based modeling of impedance in a wide variety of fields including corrosion,3 hydrodynamic systems,4 fuel cells,5 and lithium ion batteries.6However, despite the important role and wide acceptance of these physics-based models, their impact in experimental impedance analysis has been limited by their complexity – these models often contain many coupled partial differential equations representing the different physicochemical processes. Here we present an open-source, web-based tool for the in-depth analysis of experimental EIS spectra. We show that building a large database of simulated spectra across a wide range of parameters enables deeper insight into the electrochemical system under study. As a demonstration, we present an analysis of experimental lithium ion battery data using the widely utilized pseudo 2-dimensional (P2D) battery model.

A posteriori limiting for 2D Lagrange plus Remap schemes solving the hydrodynamics system of equations

In this article we show the gain in accuracy and robustness brought by the use of a a posteriori MOOD limiting in replacement of the classical slope limiter employed in the remap phase of a legacy second-order Lagrange+Remap scheme solving the Euler system of equations. This simple substitution ensures extended robustness property, better accuracy and ability to capture physical phenomena. Numerical tests in 2D assess those improvements and the relative low cost of this a posteriori approach by reporting the number of troubled cells which demand re-computation. Situations like the occurrence of Not-a-Number, negative density and spurious numerical oscillations can therefore be cured.

HYDRAULIC ANALYSIS OF A WATER DISTRIBUTION SYSTEM

The main function of a water distribution system (WDS) is to transport water from the treatment facility to the customers. Furthermore, distribution systems provide storage, flow and pressure suitable for the system. In this project, a water distribution system for a small village is modelled. Initial data of the water distribution system were given by the Hydrodynamic Systems Department at Budapest University of Technology and Economics. To compute the hydraulics parameters in the water distribution system and run hydraulic simulations, the software Staci was used, which was developed by the same department.

Approximation of the stochastic 2D hydrodynamical type systems driven by non-Gaussian Lévy noise

We propose and analyze a numerical scheme for the approximation of the solution for the stochastic 2D hydrodynamical type systems driven by non-Gaussian Lévy noise. We prove the convergence of the scheme which is a linear evolution equation with additive noise.

A high‐order flux reconstruction adaptive mesh refinement method for magnetohydrodynamics on unstructured grids

SummaryWe report our recent development of the high‐order flux reconstruction adaptive mesh refinement (AMR) method for magnetohydrodynamics (MHD). The resulted framework features a shock‐capturing duo of AMR and artificial resistivity (AR), which can robustly capture shocks and rotational and contact discontinuities with a fraction of the cell counts that are usually required. In our previous paper, we have presented a shock‐capturing framework on hydrodynamic problems with artificial diffusivity and AMR. Our AMR approach features a tree‐free, direct‐addressing approach in retrieving data across multiple levels of refinement. In this article, we report an extension to MHD systems that retains the flexibility of using unstructured grids. The challenges due to complex shock structures and divergence‐free constraint of magnetic field are more difficult to deal with than those of hydrodynamic systems. The accuracy of our solver hinges on 2 properties to achieve high‐order accuracy on MHD systems: removing the divergence error thoroughly and resolving discontinuities accurately. A hyperbolic divergence cleaning method with multiple subiterations is used for the first task. This method drives away the divergence error and preserves conservative forms of the governing equations. The subiteration can be accelerated by absorbing a pseudo time step into the wave speed coefficient, therefore enjoys a relaxed CFL condition. The AMR method rallies multiple levels of refined cells around various shock discontinuities, and it coordinates with the AR method to obtain sharp shock profiles. The physically consistent AR method localizes discontinuities and damps the spurious oscillation arising in the curl of the magnetic field. The effectiveness of the AMR and AR combination is demonstrated to be much more powerful than simply adding AR on finer and finer mesh, since the AMR steeply reduces the required amount of AR and confines the added artificial diffusivity and resistivity to a narrower and narrower region. We are able to verify the designed high‐order accuracy in space by using smooth flow test problems on unstructured grids. The efficiency and robustness of this framework are fully demonstrated through a number of two‐dimensional nonsmooth ideal MHD tests. We also successfully demonstrate that the AMR method can help significantly save computational cost for the Orszag‐Tang vortex problem.

Modified additive-averaged splitting for solving three-dimensional equations of hydrodynamics

Hydrodynamic equations form the basis of modern ecological and meteorological models. The complexity of the implementation of such models is due to three-dimensionality and nonlinearity of the equations, as well as large amounts of data and the need for prompt solutions. The use of parallel computing for solving hydrodynamic systems entered in the world practice. This approach makes it possible to reduce solution time significantly, but requires the development of new methods of implementation of the model equations. The described method for solving three-dimensional equations of convective diffusion is a modification of additive-averaged splitting three-dimensional equations. The modification carried out to increase the efficiency of splitting for the parallel computing. The essence of the modification is the introducing a parameter that indicates the number of steps, on which one-dimensional problems are solved by an explicit account in parallel on different processors without exchange of data between them. The results of numerical experiments that confirm the good accuracy, convergence and efficiency of the proposed method are shown.

Simple and Fast Determination of Warfarin in Pharmaceutical Samples Using Boron‐doped Diamond Electrode in BIA and FIA Systems with Multiple Pulse Amperometric Detection

AbstractThis paper proposes the use of the boron‐doped diamond electrode (BDDE) in flow and batch injection analysis (FIA and BIA) systems with multiple‐pulse amperometric (MPA) detection for the determination of warfarin (WA) in pharmaceutical formulations. The electrochemical behavior of WA obtained by cyclic voltammetry (CV) in 0.1 mol L−1 phosphate buffer shows an irreversible oxidation process at +1.0 V (vs Ag/AgCl). The MPA was based on the application of two sequential potential pulses as a function of time on BDDE: (1) for WA detection at +1.2 V/100 ms and; (2) for electrode surface cleaning at −0.2 V/200 ms. Both hydrodynamic systems (FIA‐MPA and BIA‐MPA) used for WA determination achieved high precision (with relative standard deviations around 2 %, n=10), wide linear range (2.0−400.0 μmol L−1), low limits of detection (0.5 μmol L−1) and good analytical frequency (94 h−1 for FIA and 130 h−1 for BIA). The WA determination made by the proposed methods was compared to the official spectrophotometric method. The FIA‐MPA and BIA‐MPA methods are simple and fast, being an attractive option for WA routine analysis in pharmaceutical industries.

Energy spectrum of oscillations in generalized Sagdeev potential

In this paper, the full energy spectrum of nonlinear oscillations, known as the cnoidal waves, is studied in the framework of small-amplitude Korteweg de Vries and modified Korteweg de Vries (mKdV) theories based on the pseudoparticle motion in Helmholtz and Duffing potentials by employing the newly introduced pseudoenergy concept. The pseudoenergy dependence of various cnoidal oscillation parameters is then studied, and it is shown that superposition of cnoidal waves leads to familiar beating and Lissajous profiles. One of the most important aspects of the nonlinear oscillation is found to be the frequency dependence of the oscillation amplitude which mainly characterizes the nature of oscillations. It is shown that the developed method can be used to study the spectrum of oscillations and shock waves in the fully nonlinear Sagdeev pseudopotential and to directly calculate many dynamic parameters of the given nonlinear system. Current research may be helpful in understanding of basic excitations and interaction of nonlinear oscillation in various hydrodynamic systems including plasmas. It is also shown that nonlinear excitations in a hydrodynamic fluid can be effectively investigated by close inspection of shock waves which contain the full nonlinear spectrum of dynamical systems.

Rayleigh–Bènard convection in the generalized Oberbeck–Boussinesq system

The original Oberbeck–Boussinesq (OB) equations which are the coupled two dimensional Navier–Stokes(NS) and heat conduction equations have been investigated by E.N. Lorenz half a century ago with Fourier series and opened the way to the paradigm of chaos. In our former study—Chaos, Solitons and Fractals 78, 249 (2015)—we presented fully analytic solutions for the velocity, pressure and temperature fields with the aim of the self-similar Ansatz and gave a possible explanation of the Rayleigh–Bènard convection cells. Now we generalize the Oberbeck–Boussinesq hydrodynamical system, going beyond the first order Boussinesq approximation and consider a non-linear temperature coupling. We investigate more general, power law dependent fluid viscosity or heat conduction material equations as well. Our analytic results obtained via the self-similar Ansatz may attract the interest of various fields like meteorology, oceanography or climate studies.

Henri Bénard: Thermal convection and vortex shedding

We present in this article the work of Henri Bénard (1874–1939), a French physicist who began the systematic experimental study of two hydrodynamic systems: the thermal convection of fluids heated from below (the Rayleigh–Bénard convection and the Bénard–Marangoni convection) and the periodical vortex shedding behind a bluff body in a flow (the Bénard–Kármán vortex street). Across his scientific biography, we review the interplay between experiments and theory in these two major subjects of fluid mechanics.

NUMERICAL MODELING OF NON-COHESIVE CONTACT IN MULTI-BODY HYDRODYNAMIC SYSTEMS WITH SPH

Enforcing solid boundary conditions is one of the most challenging parts of the Smoothed Particle Hydrodynamics (SPH) method and many different approaches have been recently developed. Better understanding of interaction forces between solid bodies is of great importance in the investigation of structural stability and armor layer displacement in breakwaters. In this study, performance of repulsive force and dynamic boundary conditions have been investigated and showed that non-physical results are presented in non-cohesive contact. In this paper, a non-cohesive contact model in multi-body hydrodynamic systems has been developed and validated against other common boundary conditions. Using the developed contact model, the effect of regular and irregular placement of cubic concrete armors has been investigated. Also, comparison has been made with Van Buchem (2009) experimental results and concluded that in the irregular case it is more possible that a unit moves toward instability.

Influence of dissimilar radial clearances on the performance of hydrodynamic rotor-bearing systems considering misalignment effects

Influence of dissimilar radial clearances of the two end bearings on the performance of hydrodynamic rotor-bearing systems is investigated in the present paper. The rotor misalignment effects are considered. A parameter ξ is introduced to measure the dissimilar level and three typical applied points ( Case Left, Case Center, and Case Right) of external load are also investigated during the analysis. Finite difference method is adopted to solve the Reynolds-type equation and verification of the solution technique is conducted by comparison with previous work. The rotor equilibrium postures are solved at different dissimilar parameters ( ξ) for the three external loading situations. Results show that dissimilar radial clearances have significant effects on rotor postures, minimum film thickness, stiffness and damping coefficients. Under unbalanced load situations ( Case Right, Case Left), small values of ξ (<1.0) will alleviate and large one ξ (>1.0) will aggravate the misaligned effects. Meanwhile, the minimum film thickness increases with ξ (<1.0) and decreases with ξ (>1.0). For stiffness and damping coefficients, the variations with ξ have no obvious rules. During the design and analysis of hydrodynamic rotor-bearing systems, the dissimilarity should be considered intensively for reaching appropriate results.

Jordan form, parabolicity and other features of change of type transition for hydrodynamic type systems

Changes of type transitions for two-component hydrodynamic type systems are discussed. It is shown that these systems generically assume the Jordan form (with Jordan block) on the transition line with hodograph equations becoming parabolic. Conditions which allow or forbid the transition from the hyperbolic domain to elliptic one are discussed. Hamiltonian systems and their special subclasses and equations, such as dispersionless nonlinear Schrödinger, dispersionless Boussinesq, one-dimensional isentropic gas dynamics equations, and nonlinear wave equations are studied. Numerical results concerning the crossing of transition line for the dispersionless Boussinesq equation are also presented.

Acoustic-hydrodynamic-flame coupling—A new perspective for zero and low Mach number flows

A combustion chamber has a hydrodynamic field that convects the incoming fuel and oxidizer into the chamber, thereby causing the mixture to react and produce heat energy. This heat energy can, in turn, modify the hydrodynamic and acoustic fields by acting as a source and thereby, establish a positive feedback loop. Subsequent growth in the amplitude of the acoustic field variables and their eventual saturation to a limit cycle is generally known as thermo-acoustic instability. Mathematical representation of these phenomena, by a set of equations, is the subject of this paper. In contrast to the ad hoc models, an explanation of the flame-acoustic-hydrodynamic coupling, based on fundamental laws of conservation of mass, momentum, and energy, is presented in this paper. In this paper, we use a convection reaction diffusion equation, which, in turn, is derived from the fundamental laws of conservation to explain the flame-acoustic coupling. The advantage of this approach is that the physical variables such as hydrodynamic velocity and heat release rate are coupled based on the conservation of energy and not based on an ad hoc model. Our approach shows that the acoustic-hydrodynamic interaction arises from the convection of acoustic velocity fluctuations by the hydrodynamic field and vice versa. This is a linear mechanism, mathematically represented as a convection operator. This mechanism resembles the non-normal mechanism studied in hydrodynamic theory. We propose that this mechanism could relate the instability mechanisms of hydrodynamic and thermo-acoustic systems. Furthermore, the acoustic-hydrodynamic interaction is shown to be responsible for the convection of entropy disturbances from the inlet of the chamber. The theory proposed in this paper also unifies the observations in the fields of low Mach number flows and zero Mach number flows. In contrast to the previous findings, where compressibility is shown to be causing different physics for zero and low Mach number flows, we show that the heat release rate can also introduce the distinction between the zero and low Mach number flows. Therefore, during the thermo-acoustic interaction, we should consider the coupling of convection modes that arise from the interaction of acoustic and hydrodynamic fields with the entropy modes.

Vorticity generation in the Universe: A perturbative approach

We compute the generation of vorticity from velocity dispersion in the dark matter fluid. For dark matter at zero temperature Helmholtz's theorem dictates that no vorticity is generated and we therefore allow the dark matter fluid to have a non-vanishing velocity dispersion. This implies a modification to the usual hydrodynamical system (continuity and Euler equations): we have to consider the Boltzmann hierarchy up to the second moment. This means that the Euler equation is modified with a source term that describes the effect of non-zero velocity dispersion. We write an equation for the Eulerian vorticity in Lagrangian coordinates and show that it has a growing mode already at second order in perturbation theory. We compute the power spectrum of the vorticity and the rotational velocity at second order in perturbation theory.

On random pressure pulses in the turbine draft tube

The flow in the conical part of the hydroturbine draft tube undergoes various instabilities due to deceleration and flow swirling at off-design operation points. In particular, the precessing vortex rope develops at part-load regimes in the draft tube. This rope induces periodical low-frequency pressure oscillations in the draft tube. Interaction of rotational (asynchronous) mode of disturbances with the elbow can bring to strong oscillations in the whole hydrodynamical system. Recent researches on flow structure in the discharge cone in a regime of free runner had revealed that helical-like vortex rope can be unstable itself. Some coils of helix close to each other and reconnection appears with generation of a vortex ring. The vortex ring moves toward the draft tube wall and downstream. The present research is focused on interaction of vortex ring with wall and generation of pressure pulses.

Dynamic interference of two anti-phase flapping foils in side-by-side arrangement in an incompressible flow

A two-dimensional computational hydrodynamic model is developed to investigate the propulsive performance of a flapping foil system in viscous incompressible flows, which consists of two anti-phase flapping foils in side-by-side arrangement. In the simulations, the gap between the two foils is varied from 1.0 to 4.0 times of the diameter of the semi-circular leading edge; the amplitude-based Strouhal number is changed from 0.06 to 0.55. The simulations therefore cover the flow regimes from negligible to strong interference in the wake flow. The generations of drag and thrust are investigated as well. The numerical results reveal that the counter-phase flapping motion significantly changes the hydrodynamic force generation and associated propulsive wake. Furthermore, the wake interference becomes important for the case with a smaller foil-foil gap and induces the inverted Bénard von Kármán vortex streets. The results show that the hydrodynamic performance of two anti-phase flapping foils can be significantly different from an isolated pitching foil. Findings of this study are expected to provide new insight for developing hydrodynamic propulsive systems by improving the performance based on the foil-foil interaction.