Lagrangian Technique Research Articles

Reynolds number dependence of particle transport in a 90° bend with electrostatic effects

In this work, particle transport in a fully developed turbulent 90° bend flow at the “electrostatic equilibrium” state is simulated using large eddy simulation coupled with Lagrangian particle tracking technique. The flow Reynolds numbers (based on bulk velocity) considered is from 34000 to 58000. Three particle size 5, 10 and 50 μm are considered and their corresponding St number are from 2.2 to 547. Simulation results of the bend flow agree well with experimental data. The electrostatic field formed in the bend is symmetric in the spanwise direction but asymmetric in the vertical direction and radial direction, which is independent of Reynolds number. The minimum electrostatic field strength occurs at r/ra = 0.25 near the inner wall of the bend. Particles transported in a bend gradually accumulate near the wall due to turbophoresis, such trend is improved by electrostatics. In addition, under the effect of electrostatics, the plume pattern of particle distribution disappeared. Particle concentration at the inner wall of the bend is higher than that at the outer wall, which depends on the combined effect of electrostatics and Dean vortices in the bend.

Utilisation of Initialised Observation Scheme for Multi-Joint Robotic Arm in Lyapunov-Based Adaptive Control Strategy

In this paper, we present a modelling, dynamic analysis, and controller tuning comparison for a five-degree-of-freedom (DoF) multi-joint robotic arm based on the Lyapunov-based Adaptive Controller (LAC). In most pick-and-place applications of robotic arms, it is essential to control the end-effector trajectory to reach a precise target position. The kinematic solution of the 5-DoF robotic arm has been determined by the Lagrangian technique, and the mathematical model of each joint has been obtained in the range of motion condition. The Proportional-Integral-Derivative (PID) control parameters of the LAC have been determined by the Lyapunov stability approach and are initialised by four observation methods based on the obtained transfer function. The effectiveness of the initialised controller’s parameters is compared by a unit step response as the desired input of the controller system. As a result, the average error (AE) for Ziegler–Nichols is 6.6%, 83%, and 53% lower than for Pettit & Carr, Chau, and Bucz. The performance of LAC for the robotic arm model is validated in a virtual 3D model under a robot operating system environment. The results of root mean square error by LAC are 0.021 (rad) and 0.025 (rad) for joint 1 and joint 2, respectively, which indicate the efficiency of the proposed LAC strategy in reaching the predetermined trajectory and the potential of minimizing the controller tuning complexity.

Optimal management strategy for a shared EVs aggregator participating in electricity and frequency regulation reserves markets

The use of shared electric vehicles has spread widely in response to the global need of reducing CO2 emissions. Hence, in the literature, authors have proposed strategies to minimize the operative costs of shared EVs, such as the provision of electrical ancillary services. However, to provide these kinds of services jointly with transportation, charging/discharging and fleet management strategies are required. And, the currently available strategies from the literature do not consider shared EVs. Therefore, to fill this gap, this paper presents an optimization-based management strategy for shared EVs that provide ancillary services and sell energy, which is applied to a study case located in Colombia. Additionally, it includes the analysis of the economic contracts that should be established between the EVs operator and the energy retailer; in which, it was found that the best option for EVs operator is to purchase the energy at the stock electricity price and establish a bilateral contract for energy sales. Moreover, it suggests that EVs be charged at the early morning hours when the stock price is lowest, that the ancillary services be provided at hours with the highest stock price, and that the energy be sold at the hours in which the provision of ancillary services is not suitable. Finally, the paper suggests, from the application of a Lagrangian parametric technique, an incentive of at least $ 115 [COP/kWh], to make the electrical services competitive with the car-sharing transportation service, which is paid at a price 23 times higher, within the Colombian context.

On the closure of Collar’s triangle by optical diagnostics

An experimental methodology is proposed to study aeroelastic systems with optical diagnostics. The approach locally evaluates the three physical mechanisms that produce the forces involved in Collar’s triangle, namely aerodynamic, elastic, and inertial forces. Flow and object surface tracers are tracked by a volumetric particle image velocimetry (PIV) system based on four high-speed cameras and LED illumination. The images are analysed with Lagrangian particle tracking techniques, and the flow tracers and surface markers are separated based on the different properties of their images. The inertial and elastic forces are obtained solely analysing the motion and the deformation of the solid object, whereas the aerodynamic force distribution is obtained with pressure from PIV techniques. Experiments are conducted on a benchmark problem of fluid–structure interaction, featuring a flexible panel installed at the trailing edge of a cylinder. Data are collected in the resonant regime, where the panel exhibits a two-dimensional motion. The estimation of inertial and elastic forces is obtained enforcing a high-order polynomial fit to the surface motion and deformation. The aerodynamic loads on the panel are challenged by the need to devise adaptive boundary conditions complying with the panel motion. The closure of Collar’s triangle yields overall residuals of about one-half of the inertial force taken as reference. The simultaneous measurement of the three forces paves the way to assessing the equilibrium of forces closing the Collar’s triangle. The latter can be intended for uncertainty evaluation or, when only two forces are measured, for estimation of the remaining Collar element.Graphical

Symbiosis Between D2D Communication and Industrial IoT for Industry 5.0 in 5G mm-Wave Cellular Network: An Interference Management Approach

Industrial Internet of Things (IIoT) paves way into Industry 5.0, which incorporates human–machine collaboration, thereby making manufacturing industry efficient. As 5G architecture supports massive IoT connectivity and has higher spectrum efficiency, device-to-device (D2D) communication is favorable at 28 GHz. While transmitting data from sensors to end user through IoT network, interference affects the system. Thus, an efficient resource allocation scheme is needed for minimizing interference and increasing data rate. Here, formulated problem is divided into two subproblems, channel assignment and power optimization in order to lower computational complexity. A partial resource multiplexing scheme is proposed that will allocate channels to available D2D users. Later, power optimization problem is formulated which is determined through Lagrangian dual optimization technique. Dynamic sectorization overcomes issue of increase in user traffic. Stability factor, fairness index (FI), and energy efficiency depict the performance superiority of proposed scheme over existing schemes. Simulation results prove efficacy of proposed system.

Coolant flow in drilling titanium considering two phase boiling

In drilling titanium alloys, significant heat build-up on drill cutting edges due to insufficient heat dissipation raises tool temperature, leading to its rapid wear. Researchers have experimented with a variety of cooling methods to reduce temperature as well as tool damage. The in-situ monitoring of temperature of cutting edges presence of fluids in the drilling is difficult. Therefore, computational fluid dynamics (CFD) based model is proposed to investigate the temperature distribution along the drill cutting edges, and the flow characteristics of the cutting fluids such as water, mist and liquid nitrogen around the cutting edges. The boiling of cutting fluids near the cutting edges of the drill was considered by using Volume of Fluid (VOF) multiphase model in the analysis. The mist cooling was handled using a discrete phase model, and the Euler–Lagrangian technique was employed to deal with interactions between air and droplets. The highest vapour volume fraction of coolants was detected along the chisel edge of the drill cutting edge in flood and cryogenic cooling conditions. Whereas, for mist cooling, maximum vapour volume fraction of coolants was detected end of cutting edges. As the liquid nitrogen has an unusually low boiling point, it undergoes a quick phase change during the initial stages of drilling. Coolant velocities around the cutting edges in flood, cryogenic, and thick-thin mist cooling were 0.03–0.12 m/s, 0.7–0.9 m/s, 4–9 m/s, and 6–13 m/s, respectively. The maximum temperature of the drill drops by 45–48%, 32–38%, 29–36%, and 24–32% in cryogenic, thick mist, thin mist and flood conditions, respectively, over the dry condition. The numerically predicted temperature lies within an error of ∼4–18% of that of the average experimental temperature.

On the wake dynamics of a cylinder with flexible splitter plate

An experimental investigation is carried out to study the effect of a flexible splitter plate on the wake dynamics of a circular cylinder. Several regimes of foil motion are imaged and identified in the range of free stream velocities 1e4 < Re < 1e5. Based on the amplitude and the span-wise coherence of the plate motion, the regimes are classified into 4 categories: low oscillations, resonance, chaotic, and bi-stable. Wind-tunnel experiments are conducted on the resonant and chaotic regimes to further explore the cylinder-plate flow. Object surface and flow tracers are tracked by a volumetric Particle Image Velocimetry system based on four high speed cameras and LED illumination. The images are analysed with Lagrangian Particle Tracking techniques and the flow tracers and surface markers are separated based on the different properties of their images. A statistical analysis of the stream-wise and transverse velocity components on the cross-sectional plane compares the pure cylinder flow to the cylinder with the trailing splitter plate. Proper Orthogonal Decomposition is applied to study the most dominant modes from each flow. Results show two different coupling mechanisms pertaining to different aeroelastic regimes. In the resonant regime, the first bending mode of the flexible plate is excited by the shedding frequency. Overall, the results showed a one-way coupling between the flow and the plate, meaning that the motion of the structure was driven by the dominant features of the flow, whereas the flow was mostly unaffected by the presence of the flexible plate. The chaotic regime is an example of full interaction, i.e. 2-way coupling between flow and structure, where the addition of the plate disrupts the shedding structures of the cylinder wake flow. The three-dimensional motion of the flexible plate enhanced the span-wise flow oscillations and so, the three-dimensional features of the wake.

Lagrangian Analysis of Moisture Sources of Precipitation in the Tianshan Mountains, Central Asia

AbstractThe moisture sources of precipitation in the Tianshan Mountains, one of the regions with the highest precipitation in Central Asia during 1979–2017 are comprehensively and quantitatively summarized by using a Lagrangian moisture source detection technique. Continental sources provide about 93.2% of the moisture for precipitation in the Tianshan Mountain, while moisture directly from the ocean is very limited, averaging only 6.8%. Central Asia plays a dominant role in providing moisture for all sub‐regions of the Tianshan Mountains. For the Western Tianshan, moisture from April to October comes mainly from Central Asia (41.4%), while moisture from November to March is derived primarily from Western Asia (45.7%). Nearly 13.0% of moisture to precipitation for Eastern Tianshan in summer originates from East and South Asia, and the Siberia region. There is a significant decreasing trend in the moisture contribution of local evaporation and Central Asia in the Eastern Tianshan during winter. The contribution of moisture from Europe to summer precipitation in the Central and Eastern Tianshan and the contribution of the North Atlantic Ocean to summer precipitation in the Northern, Central, and Eastern Tianshan also exhibit a decreasing trend. The largest increase in moisture in Western Tianshan stems from West Asia during extreme winter precipitation months. Europe is also an important contributor to extreme precipitation in the Northern Tianshan. The moisture from East and South Asia and Siberia during extreme precipitation months in both winter and summer is significantly enhanced in the Eastern Tianshan.

Simulating cold shear flows on a moving mesh

ABSTRACT Rotationally supported, cold, gaseous discs are ubiquitous in astrophysics and appear in a diverse set of systems, such as protoplanetary discs, accretion discs around black holes, or large spiral galaxies. Capturing the gas dynamics accurately in these systems is challenging in numerical simulations due to the low sound speed compared to the bulk velocity of the gas, the resolution limitations of full disc models, and the fact that numerical noise can easily source spurious growth of fluid instabilities if not suppressed sufficiently well, negatively interfering with real physical instabilities present in such discs (like the magnetorotational instability). Here, we implement the so-called shearing-box approximation in the moving-mesh code arepo in order to facilitate achieving high resolution in local regions of differentially rotating discs and to address these problems. While our new approach offers manifest translational invariance across the shearing-box boundaries and offers continuous local adaptivity, we demonstrate that the unstructured mesh of arepo introduces unwanted levels of ‘grid-noise’ in the default version of the code. We show that this can be rectified by high-order integrations of the flux over mesh boundaries. With our new techniques we obtain highly accurate results for shearing-box calculations of the magnetorotational instability that are superior to other Lagrangian techniques. These improvements are also of value for other applications of the code that feature strong shear flows.

Run-to-Tumble Variability Controls the Surface Residence Times of E. coli Bacteria.

Motile bacteria are known to accumulate at surfaces, eventually leading to changes in bacterial motility and biofilm formation. We use a novel two-color, three-dimensional Lagrangian tracking technique to follow simultaneously the body and the flagella of a wild-type Escherichia coli. We observe long surface residence times and surface escape corresponding mostly to immediately antecedent tumbling. A motility model accounting for a large behavioral variability in run-time duration reproduces all experimental findings and gives new insights into surface trapping efficiency.

Modelling of binary fluidization of coal and ash and validation using radioactive particle tracking and densitometry

AbstractBinary fluidization finds wide application in a variety of gas–solid catalytic and non‐catalytic industrial fluidization systems. In the present study, a three‐dimensional transient computational fluid dynamics (CFD) model was used to model the binary fluidization of coal and ash in a laboratory‐scale cold flow fluidized bed. In parallel, phase velocity measurements using radioactive particle tracking (RPT) and gamma‐ray densitometry were performed, which provided a rich database for validation of the CFD model. RPT being a time‐resolved Lagrangian technique, it was possible to extract velocity fluctuations and their correlations in addition to the mean velocity profiles. The latter provided additional validation for the CFD model, in addition to the typical validation that is done with time‐averaged profiles of phase velocity and volume fraction. The robust validation procedure opens up the possibility of expanding this model to a pilot plant‐scale fluidized bed.

Optimal unit-commitment generation scheduling using genetic algorithm: A case study of a 10-generator power system network

Generation Scheduling is a complex optimisation problem. The aim is to get an optimal combination of generating units for optimal operation. In this paper, Genetic Algorithm (GA) is presented as a viable optimisation tool to solve a fuel cost-based unit-commitment problem. The power system network adopted for the study is a 10-generator network. The prime objective here is to prepare the best economic start-up and shutdown schedules of the generators which meets the forecasted load demand plus reserve for a particular time interval while at the same time satisfying various system constraints. The implementation was done with the GA Toolbox in MATLAB 2018a. Results obtained were compared to the ones obtained with Lagrangian Relaxation optimisation technique and the comparison shows that Genetic Algorithm led to a slight reduction in fuel cost by ₦ 522,452.20 for the 24-hour period.

Deep Learning Aided Physical-Layer Security: The Security Versus Reliability Trade-Off

This paper considers a communication system whose source can learn from channel-related data, thereby making a suitable choice of system parameters for security improvement. The security of the communication system is optimized using deep neural networks (DNNs). More explicitly, the associated security vs reliability trade-off problem is characterized in terms of the symbol error probabilities and the discrete-input continuous-output memoryless channel (DCMC) capacities. A pair of loss functions were defined by relying on the Lagrangian and on the monotonic-function based techniques. These were then used for managing the learning/training process of the DNNs for finding near-optimal solutions to the associated non-convex problem. The Lagrangian technique was shown to approach the performance of the exhaustive search. We concluded by characterizing the security vs reliability trade-off in terms of the intercept probability vs the outage probability.

Solving the reliability-oriented generalized assignment problem by Lagrangian relaxation and Alternating Direction Method of Multipliers

The well-known generalized assignment problem has many real-world applications. The assignment costs between agents and tasks affected by several factors could be unstable and uncertain. In this paper, we assume that the means and variances of assignment costs are known in advance. The idea is that the decision-maker aims to minimize the total assignment costs not only on average, but also to keep their variability as small as possible. Then, a reliability-oriented model with a nonlinear and concave objective function is formulated, and two decomposition-based methods are systematically developed for this challenging problem. The task allocation constraints are dualized and the Lagrangian relaxed problem is broken into many reliability-oriented knapsack subproblems. By the Lagrangian substitution technique, each subproblem is further decomposed into a standard knapsack problem and a simple univariate concave minimization problem. A lower bound is constructed and multipliers are optimized in dual problems by the subgradient method. Feasible solutions can be generated from the results of these reliability-oriented subproblems by Lagrangian heuristic. To further improve the convergence and solution quality, an Alternating Direction Method of Multipliers (ADMM) based decomposition approach is proposed. The augmented Lagrangian relaxed problem is split into a sequence of subproblems by the block coordinate descent method. To cope with the quadratic terms and the concave terms in these subproblems, linearization and Lagrangian substitution techniques are applied. Feasible solutions are produced from these subproblems, and solution quality can be evaluated by the lower bound provided by the Lagrangian relaxed problem. Numerical experiments are conducted on the test cases transformed from the standard benchmark instances, and the ADMM-based method has superior convergence and solution quality.

Linear and weakly nonlinear dominant dynamics in a boundary layer flow

The aim of this paper is to investigate the linear and weakly nonlinear dynamics in flow over a flat-plate with leading edge. Linear optimal and suboptimal inflow perturbations are obtained using a Lagrangian multiplier technique. In particular, the suboptimal inflow conditions and the corresponding downstream responses are investigated in detail for the first time. Unlike the suboptimal dynamics reported in other canonical cases such as the backward-facing step flow, the growth rate of the suboptimal perturbation is in the same order as the optimal one, and both of them depend on the lift-up mechanism even though they are orthogonal. The suboptimal mode has an additional layer of vorticity that penetrates into the boundary layer farther downstream, generating a second patch of high- and low-speed streaks. The farther suboptimal ones spread to the free-stream without entering the boundary layer. The weakly nonlinear dynamics are examined by decomposing the flow field into multiple orders of perturbations using the Volterra series. Small structures in the higher order perturbations mainly concentrate in the region farther away from wall, suggesting a mechanism of outward perturbation developments, which is opposite with the well reported inward development of perturbations, i.e., from free-stream to boundary layer. The significance of these modes is then demonstrated through a prediction of flow field from the inflow condition by exploiting the orthogonality of the modes.

Sediment and Radioactivity Transport in the Bohai, Yellow, and East China Seas: A Modeling Study

This paper is concerned with the development of a radionuclide dispersion model for the nuclear power plants in the Bohai, Yellow, and East China seas (BYECS) characterized by high turbidity and multi-scale circulations, focusing on the comparison of dispersion processes of 137Cs depending upon, in particular, the suspended sediment concentration and erosion/sedimentation processes. The simulations were carried out using a multi-fraction sediment transport model embedded in the semi-implicit Eulerian–Lagrangian finite-element coupled wave-circulation model linked with the model of radionuclide transport, which describes the key radionuclide transfer processes in the system of water–multi-fraction sediments. In contrast to the Eulerian models used for hydrodynamics and sediment transport processes, the Lagrangian technique was applied to simulate the transport of radionuclides. The simulation results for total suspended concentration agreed with in situ measurements and the Geostationary Ocean Color Imager data. The results of the simulation of hypothetical releases of 137Cs from four nuclear power plants (NPPs) placed in BYECS essentially differ from the real release of activity in the Pacific Ocean shelf due to the Fukushima Daiichi accident, which took place at the same time and released activity that was similar. The total amount of bottom contamination of 137Cs in releases from the Sanmen, Hanbit, and Hongyanhe NPPs was about 40% of dissolved component, and the total amount of suspended component was about 20% of dissolved component, in contrast with the Fukushima Daiichi accident, where the particulate component was only 2%. The results demonstrate the importance of erosion processes in the budget of 137Cs in shallow areas around the Sanmen and Hanbit NPPs, where strong wind and tidal currents took place.

Computational characterization of the behavior of a saliva droplet in a social environment

The conduct of respiratory droplets is the basis of the study to reduce the spread of a virus in society. The pandemic suffered in early 2020 due to COVID-19 shows the lack of research on the evaporation and fate of droplets exhaled in the environment. The current study, attempts to provide solution through computational fluid dynamics techniques based on a multiphase state with the help of Eulerian–Lagrangian techniques to the activity of respiratory droplets. A numerical study has shown how the behavior of droplets of pure water exhaled in the environment after a sneeze or cough have a dynamic equal to the experimental curve of Wells. The droplets of saliva have been introduced as a saline solution. Considering the mass transferred and the turbulence created, the results has showed that the ambient temperature and relative humidity are parameters that significantly affect the evaporation process, and therefore to the fate. Evaporation time tends to be of a higher value when the temperature affecting the environment is lower. With constant parameters of particle diameter and ambient temperature, an increase in relative humidity increases the evaporation time. A larger particle diameter is consequently transported at a greater distance, since the opposite force it affects is the weight. Finally, a neural network-based model is presented to predict particle evaporation time.

An augmented Lagrangian relaxation method for the mean-standard deviation based vehicle routing problem

With the ever-increasing trip demand and limited transportation resource, traffic congestions remain a tricky problem. Under traffic congestions, travel times are unstable and variable in a real-world network. When we conduct many time-sensitive vehicle routing optimizations such as vaccine transportation, it is essential to consider the travel time variability in these optimizations. However, most previous vehicle routing studies neglected the travel time variability and adopted the expected travel times or lengths of links. The historical travel times of multiple days allow us to access and describe the travel time variability. We can easily obtain the travel time means and standard deviations of links from these data. This study applies these two statistical indicators to vehicle routing optimization and concentrates on a mean-standard deviation based vehicle routing model. This model has a nonlinear and concave objective function that dramatically increases the problem complexity. We develop a novel augmented Lagrangian relaxation approach for this problem. A lower bound is constructed for this problem by applying the Lagrangian relaxation and decomposition technique twice. To break the inherent symmetry of this problem, we use the augmented Lagrangian relaxation method with block coordinate descent, linearization, and Lagrangian substitution techniques to achieve high-quality feasible solutions. Thus, the relative gap between the lower and upper bounds can be evaluated and reduced in the solving procedure. We implement the proposed method on the datasets modified from the standard benchmark instances. The average relative gaps of instances in sets A and P are 8.8% and 7.6%, respectively.

Local Well-Posedness of a Two-Component Novikov System in Critical Besov Spaces

In this paper, we establish the local well-posedness for a two-component Novikov system in the sense of Hadamard in critical Besov spaces Bp,11+1p(R)×Bp,11+1p(R),1≤p<∞. We first provide a uniform bound for the approximate solutions constructed by iterative scheme, then we show the convergence and regularity; afterwards, based on the Lagrangian coordinate transformation techniques, we prove the uniqueness result; finally, we show that the the solution map is continuous.

Galerkin-based finite strain analysis with enriched radial basis interpolation

We present an enriched radial basis function (RBF) interpolation, which is combined with a symmetric Galerkin method to solve finite strain problems. Specifically, Wendland compact support radial basis functions (RBF) are enriched with a quadratic polynomial, whose parameters are condensed-out during the shape-function construction phase. A total Lagrangian technique is adopted and for finite strain plasticity the formalism with the Mandel stress is adopted. These recent developments are especially convenient from the implementation perspective, as RBF formulations for finite strain plasticity have been limited by interpolation updating. We also note that, although tetrahedra are adopted for quadrature in the undeformed configuration, mesh deformation is of no consequence for the results. Four benchmark tests are successfully solved, with extensive convergence studies and showing clear advantages with respect to finite-element in terms of robustness and with respect to classical Element-Free Galerkin (EFG) formulations in terms of efficiency.