Fluid Dynamical Systems Research Articles

Formation Flight in Complex Environments Using an Artificial Potential Field

Studied here is the problem of multiple unmanned aerial vehicles flying in formation in an environment containing many obstacles and threats. Two schemes are proposed for avoiding obstacles: formation dissolution and formation change. The improved interfered fluid dynamical system approach is used to guide the unmanned aerial vehicles to their destination safely, and an artificial potential field is used for formation forming and re-forming and to avoid intervehicle collisions. Straightforward and effective control algorithms are designed for the two schemes. Unlike other algorithms, the proposed method can be applied to different scenarios with no additional requirements, such as having to have different controllers for different situations. Finally, two simulation experiments are provided to validate the effectiveness of the proposed control algorithms.

Port-Hamiltonian modelling of fluid dynamics models with variable cross-section

Many single- and multi-phase fluid dynamical systems are governed by non-linear evolutionary equations. A key aspect of these systems is that the fluid typically flows across spatially and temporally varying cross-sections. We, first, show that not any choice of state-variables may be apt for obtaining a port-Hamiltonian realization under spatially varying cross-section. We propose a modified choice of the state-variables and then represent fluid dynamical systems in port-Hamiltonian representations. We define these port-Hamiltonian representations under spatial variation in the cross-section with respect to a new proposed state-dependent and extended Stokes- Dirac structure. Finally, we account for temporal variations in the cross-section and obtain a suitable structure that respects key properties, such as, for instance, the property of dissipation inequality.

Molecular Dynamics Study of Anti-Wear Erosion and Corrosion Protection of PTFE/Al2O3 (010) Coating Composite in Water Hydraulic Valves

Cavitation erosion and corrosion commonly occur on the surface of fluid dynamic system components, mostly water hydraulic valves, causing the failure of metal parts. Coating of polytetrafluoroethylene (PTFE) on Al2O3 (010) was created by varying the chain length of polytetrafluoroethylene. Calculations were conducted by molecular dynamic (MD) simulations. This study shows that the K10 and K20 chain lengths’ mechanical properties possess negative elastic, shear, and bulk modulus values. We have found that the K10 chain length composition shows the high results of binding energy and negative bulk modulus of 6267.16 kJ/mol and −3709.54 GPa, respectively. The K10 chain length was observed to possess a higher cohesive energy density (CED) and solubility parameter of (6.885 ± 0.00076) × 109 J/m3 and (82.974 ± 0.005) (J/cm3)0.5, respectively. It was also found that increasing the chain length contributes to decreasing the binding energy and solubility parameter of PTFE/Al2O3 (010) composition. These results are vital for overcoming the repetitive regime of high compressive strength of water microjets on the valves’ material surface. Improved values of the cohesive energy density and solubility parameters imply the water’s superior hydrophobic effect.

On obstacle avoidance path planning in unknown 3D environments: A fluid-based framework

Compared with preprocessed obstacle environments, unknown environments are more challenging for path planning. In unknown environments, an agent can make decisions only by relying on the obstacle information detected by its onboard sensors. However, when facing non-convex obstacles, this limited detection information can easily trap the agent in a local optimum. In this paper, a nature-inspired methodology called Interfered Fluid Dynamic System (IFDS) is extended to anti-local-optimum obstacle avoidance in unknown 3D environments for the first time and a novel fluid-based path planning framework is proposed. First, the detection region of the agent is discretized. Then, spherical virtual obstacles (SVOs) located at detected discrete points are generated and memorized. Thus, obstacle avoidance in unknown environments is transformed into the avoidance of known SVOs. Next, the currently generated and memorized SVOs are input to the core of the framework, the IFDS algorithm, to produce repulsive effects, and the corresponding 3D avoidance path is resolved. On this basis, to address local optimum in cases with non-convex obstacles, and considering compatibility with the IFDS, the direction coefficient and sink-heading angular rate adjustment strategies, which belong to the same system as the IFDS, are introduced to modify the IFDS in this framework. Finally, receding horizon control is introduced to improve the obstacle avoidance performance. Simulations show that the proposed framework can enable the agent to autonomously jump out of the 3D non-convex obstacle environments with typical features of the local optimum, including wall-like and cave-like obstacles, and safely reach the destination.

A Simple Numerical Model for Studying Cloud Formation Process Inthe Tropics : Heated and Cooled Surface Experiments

A simple numerical model for demonstrating local cloud formation processes in the tropics is beingdeveloped. The model equations are derived from the fundamental system of partial differential equations ofcomputational fluid dynamics and the deep convection approximation is used to eliminate sound waves. Themodel domain is two-dimensional with length100 kilometers and height 17.5 kilometers. A non-uniform grid isused with the thinnest layer (100 meters) at the earth's surface and thickest layer (1,300 meters) at the top of thetroposphere. The horizontal cell's width one kilometer. The Arakawa-C grid is used for the leapfrog method andforward Euler method. Experiments to study the effects of heating and cooling at the surface and the deepconvection approximation in moist air are discussed. The deep convection approximation was found to beunsuitable for a model. The model without the deep convection approximation gives processes expected in thereal atmosphere.

Partial Differential Equations and Infinite Dimensional Dynamic Systems in Marine Fluid Dynamics

Cheng, X., 2020. Partial differential equations and infinite dimensional dynamic systems in marine fluid dynamics. In: Li, L. and Huang, X. (eds.), Sustainable Development in Coastal Regions: A Perspective of Environment, Economy, and Technology. Journal of Coastal Research, Special Issue No. 112, pp. 363-366. Coconut Creek (Florida), ISSN 0749-0208.In the analysis of massive hydrodynamics, we use the form of partial differential equations, which can conduct a comprehensive analysis of its dynamic system and obtain the corresponding circulation pattern of ocean currents, which can be more effective for some hydrodynamics. Analysis, in marine fluid mechanics, it includes a variety of hydrodynamic forces such as inertia viscosity, we can analyze and study them separately to get a more complete and systematic hydrodynamic research program. Fluids generally include liquids and gases, which are closely related to human daily life and social development. Fluid mechanics has typical physical properties and through practice can better deepen the understanding of the subject. Therefore, in the teaching of modern fluid mechanics, the experiment of fluid mechanics has become a typical supporting course in the course of fluid mechanics.

Exact relations between Rayleigh–Bénard and rotating plane Couette flow in two dimensions

Abstract

Interface learning in fluid dynamics: Statistical inference of closures within micro–macro-coupling models

Many complex multiphysics systems in fluid dynamics involve using solvers with varied levels of approximations in different regions of the computational domain to resolve multiple spatiotemporal scales present in the flow. The accuracy of the solution is governed by how the information is exchanged between these solvers at the interface, and several methods have been devised for such coupling problems. In this Letter, we construct a data-driven model by spatially coupling a microscale lattice Boltzmann method (LBM) solver and macroscale finite difference method (FDM) solver for reaction–diffusion systems. The coupling between the micro–macro-solvers has one to many mapping at the interface leading to the interface closure problem, and we propose a statistical inference method based on neural networks to learn this closure relation. The performance of the proposed framework in a bifidelity setting partitioned between the FDM and LBM domains shows its promise for complex systems where analytical relations between micro–macro-solvers are not available.

A Novel Greedy FluidSpread Algorithm With Equilibrium Temperature for Influence Diffusion in Social Networks

Maximizing positive influenced users (MPIU) is one of the most important and classic problems in social networks. In this article, we propose an effective solution to the problem of MPIU with positive top- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> influence, namely, Greedy FluidSpread Algorithm with Equilibrium Temperature (GFAET). In this article, the behavior of the users, such as the interactions and relationships of each user, and the content of a topic are modeled to the user interest vector and the topic distribution vector, respectively, to calculate the information acceptance probability. The influence diffusion process in social network is modeled as a fluid dynamics system and the attitude of the user is modeled as the fluid temperature. Newton's law of cooling and fluid dynamics theory is utilized to obtain a more accurate value of equilibrium temperature. Important users are then greedily selected in this system. Extensive experiments demonstrate that our GFAET significantly outperforms other traditional methods in terms of positive influence spread on both artificially generated and real-trace network datasets.

Multibody Dynamics Versus Fluid Dynamics: Two Perspectives on the Dynamics of Granular Flows

Abstract Considering that granular material is second only to water in how often it is handled in practical applications, characterizing its dynamics represents a ubiquitous problem. However, studying the motion of granular material poses stiff computational challenges. The underlying question in this contribution is whether a continuum representation of the granular material, established in the framework of the smoothed particle hydrodynamics (SPH) method, can provide a good proxy for the fully resolved granular dynamics solution. To this end, two approaches described herein were implemented to run on graphics processing unit (GPU) cards to solve the three-dimensional (3D) dynamics of the granular material via two solution methods: a discrete one, and a continuum one. The study concentrates on the case when the granular material is packed but shows fluid-like behavior under large strains. On the one hand, we solve the Newton–Euler equations of motion to fully resolve the motion of the granular system. On the other hand, we solve the Navier–Stokes equations to describe the evolution of the granular material when treated as a homogenized continuum. To demonstrate the similarities and differences between the multibody and fluid dynamics, we consider three representative problems: (i) a compressibility test (highlighting a static case); (ii) the classical dam break problem (highlighting high transients); and (iii) the dam break simulation with an obstacle (highlighting impact). These experiments provide insights into conditions under which one can expect similar macroscale behavior from multibody and fluid dynamics systems governed by manifestly different equations of motion and solved by vastly different numerical solution methods. The models and simulation platform used are publicly available and part of an open source code called Chrono. Timing results are reported to gauge the efficiency gains associated with treating the granular material as a continuum.

Criteria for the onset of convection in the phase-change Rayleigh–Bénard system with moving melting-boundary

Here, for the first time, we report the criterion for the onset of convection in a low Prandtl number phase-change Rayleigh–Bénard (RB) system with an upward moving melt interface in a two-dimensional square box for a wide range of Rayleigh number Ra and Stefan number Ste (defined as the ratio between the sensible heat to the latent heat). High fidelity simulations were performed to study the phenomenon of the onset of convection. Unlike the classical RB system in the phase-change RB system, it was found that the onset of convection depended on Ste and Fourier number τ, in addition to Ra. The phase-change RB system with upward moving melt interface can be classified into two groups: slow expanding phase-change RB system (Ra ≤ 104) and moderate/fast melting phase-change RB system (Ra &amp;gt; 104). The slow melting phase-change RB system becomes unstable when the effective Rayleigh number based on the melt height is ≈1295.78, consistent with the finding by Vasil and Proctor [“Dynamic bifurcations and pattern formation in melting-boundary convection,” J. Fluid Mech. 686, 77 (2011)]; however, moderate and fast melting phase-change RB systems become unstable when the product of the local Rayleigh number Ra based on the melt-layer height hyt and the Fourier number based on the melt-layer height reaches a threshold value. Interestingly, it is seen that the criteria for the onset of convection for moderate and fast melting phase-change RB systems show a power law kind of form such that Racrτcr = aSteb + c. In addition, during the initial conduction regime before the onset of convection, it is seen that the Nusselt number at the hot wall is Nuh ∼ τ0.5, and during the onset of convection, i.e., during the formation of the initial convection rolls, the Nusselt number at the hot wall is Nuh ∼ τd, where the value of the exponent d is 2 for low Rayleigh numbers and 4 for higher Rayleigh numbers. This study reports some general characteristics of the onset of convection and some organized behavior in the transient melting phase-change RB system, which are not yet explored and reported in the open literature. This work may lead to significant understanding of different applications of fluid-dynamical melting phase-change RB systems in both natural and engineering systems.

Exploration and prediction of fluid dynamical systems using auto-encoder technology

Machine-learning (ML) algorithms offer a new path for investigating high-dimensional, nonlinear problems, such as flow-dynamical systems. The development of ML methods, associated with the abundance of data and combined with fluid-dynamics knowledge, offers a unique opportunity for achieving significant breakthroughs in terms of advances in flow prediction and its control. The objective of this paper is to discuss some possibilities offered by ML algorithms for exploring and predicting flow-dynamical systems. First, an overview of basic concepts underpinning artificial neural networks, deep neural networks, and convolutional neural networks is given. Building upon this overview, the concept of Auto-Encoders (AEs) is introduced. An AE constitutes an unsupervised learning technique in which a neural-network architecture is leveraged for determining a data structure that results from reducing the dimensionality of the native system. For the particular test case of flow behind a cylinder, it is shown that combinations of an AE with other ML algorithms can be used (i) to provide a low-dimensional dynamical model (a probabilistic flow prediction), (ii) to give a deterministic flow prediction, and (iii) to retrieve high-resolution data in the spatio-temporal domain from contaminated and/or under-sampled data.

A model based new method for injection rate determination

This paper presents a detailed model of a common rail diesel injector and its validation using injection rate measurement. A new method is described for injector nozzle flowrate determination using simulation and measurement tools. The injector model contains fluid dynamic, mechanic and electro-magnetic systems, describing all-important internal processes and also includes the injection rate meter model. Injection rate measurements were made using the Bosch method, based on recording the pressure traces in a length of fuel during injections. Comparing the results of the simulated injection rate meter, simulated injector orifice flow and injection rate measurements, the simulated and measured injection rates showed good conformity. In addition to this, the difference between nozzle flow rate and the measured flow rate is pointed out in different operating points, proving, that the results of a Bosch type injection rate measurements cannot be directly used for model validation. However, combining injector, injection rate meter simulation and measurement data, the accurate nozzle flow rate can be determined, and the model validated.

Data-driven versus self-similar parameterizations for stochastic advection by Lie transport and location uncertainty

Abstract. Stochastic subgrid parameterizations enable ensemble forecasts of fluid dynamic systems and ultimately accurate data assimilation (DA). Stochastic advection by Lie transport (SALT) and models under location uncertainty (LU) are recent and similar physically based stochastic schemes. SALT dynamics conserve helicity, whereas LU models conserve kinetic energy (KE). After highlighting general similarities between LU and SALT frameworks, this paper focuses on their common challenge: the parameterization choice. We compare uncertainty quantification skills of a stationary heterogeneous data-driven parameterization and a non-stationary homogeneous self-similar parameterization. For stationary, homogeneous surface quasi-geostrophic (SQG; QG) turbulence, both parameterizations lead to high-quality ensemble forecasts. This paper also discusses a heterogeneous adaptation of the homogeneous parameterization targeted at a better simulation of strong straight buoyancy fronts.

Cooperative Dynamic Fuzzy Perimeter Surveillance: Modeling and Fluid-Based Framework

In this article, considering the performance limitations of the sensors used in real missions, the cooperative dynamic fuzzy perimeter surveillance (CDFPS) problem and its fluid-based solution framework are proposed for the first time. First, the two-dimensional concentration diffusion distribution function is used to imitate an irregular dynamic perimeter. Then, according to the onboard sensor resolution ratio, a fuzzification process is applied for the perimeter area. On this basis, the detected fuzzy perimeter area is modeled with virtual obstacles (VOs). Considering an obstacle set composed of VOs, fixed obstacles and agents, we transform the CDFPS problem into a unified obstacle avoidance problem for the first time and a fluid-based path planning method is designed based on restrained interfered fluid dynamical system and Lyapunov guidance vector field. To quantify the surveillance effect, two indexes for the CDFPS problem are proposed: the perimeter neutrality index and the phase angle uniformity index. Around these proposed indexes, the attractive/repulsive effects and the multiagent cooperative mechanism are constructed. Finally, the receding horizon control is introduced to further improve the surveillance effect. Simulations show that the proposed framework can drive agents to persistently track the perimeter and establish relatively stable phase angle offsets between adjacent agents.

Light guide systems enhance microalgae production efficiency in outdoor high rate ponds

Microalgae provide a powerful solar driven biotechnology platform for the production of the increasing quantity of food, fuel, high value products, fine chemicals and clean water required to supply our expanding global population. Light capture fuels all photosynthetically driven microalgae processes and consequently, maximizing light capture efficiency at minimal cost is central to process design. Raceway-style and paddle wheel operated open ponds, also known as high rate ponds (HRP0), are widely used, easy to operate and offer low-cost evaporative cooling compared to energy intensive closed systems. Here, the concept of delivering light from the surface into greater depths of the algae solution was tested at pilot-scale, by fitting a standard HRP0 with light transmitting guides designed to allow the capture of sunlight between ~10:00 am and ~3:00 pm to improve light distribution throughout the depth of the solution (HRP+). This prototype (HRP+) was analyzed to compare light distribution and biomass production efficiency against two control systems in two separate experiments such as: 1) a standard High Rate Pond (HRP0), and 2) a standard HRP0 fitted with no light transmitting dummy guides (HRP-) to maintain comparable fluid dynamics system characteristics. Under semi-continuous cultivation, HRP+ showed a significantly improved light distribution within the culture compared to the HRP- when operated at moderate to high densities. An increased proportion of the culture in the HRP+ was kept within the desired optimal photosynthetic zones while dark zones (unfit for photosynthesis and causing biomass loss) were drastically reduced compared to the HRP-. The HRP+ system exhibited a 3.9-fold higher maximum areal productivity of 49.2 ± 8.3 g·m−2·d−1 compared to HRP- (March–April 2018). Overall, this study establishes proof-of-concept of the functionality of light guides to improve light distribution and productivities in microalgae cultivation systems compared to the control systems run at the same incident light levels.

Comprehensive Optimization of Energy Storage and Standoff Tracking for Solar-Powered UAV

Compared with traditional unmanned aerial vehicle (UAV), the solar-powered UAV (SUAV) has longer endurance by converting solar energy into electric energy. This article focuses on the comprehensive optimization of energy storage and standoff tracking performance for SUAV with application to the target tracking task. First, an adjustable Lyapunov guidance vector field (ALGVF) is proposed and combined with the interfered fluid dynamical system (IFDS) method to achieve the standoff target tracking mission in obstacle environment, making it possible to adjust the tracking trajectory flexibly. Then, the adjustment factor of ALGVF and the obstacle reaction coefficients of IFDS are optimized simultaneously to generate the optimal trajectory of SUAV, aiming to maximize the solar energy storage while minimize the tracking error. Finally, the simulation results verify the feasibility of our method and give the influence of different solar irradiance on SUAV trajectory optimization.

Low resolution modelling of mixing phenomena in PWR fuel assemblies

Simulation of single-phase turbulent flow in the entire reactor core is a challenging task due to a complex geometry and a huge computational domain, which requires large number of computational cells. In order to reduce the size of a computational mesh, simplifications in the geometry are practically inevitable. Among the most challenging parts with many small details that affect the flow through a fuel assembly are mixing grids. There are several different designs of the mixing grids. One of the most frequently used designs consists of a strap, springs and dimples, which are used as a structural support for the fuel rods, and mixing vanes, which deflect the fluid and increase the mixing. Neglecting the effects of the mixing grid would result in a less accurate reproduction of the flow and temperature field, which may lead to too small inter sub-channel mixing in the fuel assembly. Hence, application of a porosity model is proposed for the mixing grid, which largely reduces the computational mesh. Additional momentum sources mimic the effect of the mixing vanes. This approach aims to fill the gap between three-dimensional well-resolved Computational Fluid Dynamics (CFD) and one-dimensional sub-channel or system codes. As such, they are able to provide valuable insights to the flow behaviour in the reactor core.The present study examines the possibility to model the effect of the mixing grid by applying momentum sources in the governing equations. A split-type mixing grid is considered, which is one of the most frequently used designs in a Pressurized Water Reactor (PWR) fuel assembly. The applied split-type mixing grid generates a particular pattern of swirl motion within each sub-channel as well as it increases the cross flow between neighbour sub-channels of the fuel bundle. Non-homogeneous momentum sources have been applied, which mimic the deflection of the flow and blockage by the mixing vanes. The obtained pattern of the secondary flow closely resembles the secondary flow, which has been obtained with a reference CFD simulation that included all detailed geometrical aspects of the grid spacer with mixing vanes. The magnitudes of the momentum sources have been tuned to generate similar magnitudes of the secondary flow and stream-wise vorticity as observed in the results of the reference CFD simulation. In the next step, this approach has been applied on successively coarser meshes to investigate its effectivity on low resolution (very coarse) meshes. It turned out that the proposed model is able to mimic the mixing effect between the sub-channels. However, discrepancies are observed in the development of the secondary flow in the stream-wise direction. In the last step, the coolant flow in a flow domain consisting of 9 fuel assemblies is reproduced for normal conditions inside a PWR core as well as for two off-normal scenarios, which consider two different blockages at the entrance of the central fuel assembly. This approach has a promising potential to perform a CFD simulation of a realistic fluid mixing inside and between adjacent fuel assemblies in an entire PWR reactor core.

Design and CFD Analysis of the Fluid Dynamic Sampling System of the "MicroMED" Optical Particle Counter.

MicroMED is an optical particle counter that will be part of the ExoMars 2020 mission. Its goal is to provide the first ever in situ measurements of both size distribution and concentration of airborne Martian dust. The instrument samples Martian air, and it is based on an optical system that illuminates the sucked fluid by means of a collimated laser beam and detects embedded dust particles through their scattered light. By analyzing the scattered light profile, it is possible to obtain information about the dust grain size and speed. To do that, MicroMED’s fluid dynamic design should allow dust grains to cross the laser-illuminated sensing volume. The instrument’s Elegant Breadboard was previously developed and tested, and Computational Fluid Dynamic (CFD) analysis enabled determining its criticalities. The present work describes how the design criticalities were solved by means of a CFD simulation campaign. At the same time, it was possible to experimentally validate the results of the analysis. The updated design was then implemented to MicroMED’s Flight Model.

Analytical approximation to the solution of 3D rotating MHD system

Using energy methods and large Sobolev indexes, we prove analytically that for prepared initial velocity, in the case of high speed, we can solve the three-dimensional fully nonlinear rotating magnetohydrodynamic system by solving only its linear part and the two-dimensional Navier–Stokes equation. This procedure makes things easier in practice for physicists and engineers. Mathematically, our argument can be extended to other rotating fluid dynamics system and it can be proved for less regular data.