Vortex Elements Research Articles

Perancangan Sriwijaya Freshwater Aquarium Safari

The Design of Sriwijaya Freshwater Aquarium is a way to introduce freshwater aquatic biota, educate the public, and a destination in Palembang. This design expects to be able to respond to land conditions and produce an optimal design to persuade tourists. Design data were prepared by using observation, interviews, and literature study methods. The space program in this design includes main facilities (destinations), management buildings, supporting facilities and utilities. A special Space Study (SRK) is an analysis form of main facilities, and some utilities need. While the others used related sources for the type of space needed. The location choices is influenced by transportation and proximity to city landmarks and tourist destinations. The building is a concept of Tangible Metaphor with develop wave, zigzag, arch, and vortex elements as the shape of the main and supporting buildings. Through the analysis, the design of Sriwijaya Freshwater Aquarium Safari in Palembang can respond to land conditions by utilizing a strategic location, producing an optimal design by processing the character of the site and building shape. This could be an idea for supporting education about freshwater aquatic biota, and a new destination to persuade tourists to visit Palembang.

Wall-bounded flow simulation on vortex dynamics

Vortical flow animation has attracted considerable attention within the realm of computer graphics. Given that boundaries are the source of vorticity, we introduce a novel approach for the wall-bounded flow simulation in the vortex dynamics framework. We enhance the traditional Lagrangian vortex particle method in terms of boundary treatment and viscosity computation for boundary layer to furnish support for the simulation of the vortex shedding phenomenon behind the moving solids. We extend the boundary treatment strategy based on the idea of vortex generation with a reasonable placement algorithm for the generated vortex element to better satisfy the impermeability of solids. Furthermore, we modify the particle strength exchange method at solid boundaries to capture momentum transfer of moving solids. We demonstrate the efficacy of our approach by simulating a series of wall-bounded flows, such as the wake behind a delta wing and the vortex shedding behind the rotating sphere.

A new fast simulation method of wind turbine wake based on annular vortex element

A fast simulation method of wind turbine wake field based on the combination of lifting line and annular vortex elements is proposed to simulate the bound circulation on the blade by means of lifting line, and to simulate the evolution of the wake field by releasing the annular vortex elements through the blade. The method can be iterated until convergence is sufficient by distributing the vortex elements basin-wide through periodicity in the initialization stage. The accuracy and applicability conditions of the method are verified by comparing the above method with wind tunnel tests and software simulation results using different methods. The method is clear and simple, with low computational cost and high computational accuracy.

Numerical simulations of bio-inspired approaches to enhance underwater swimming efficiency

The present study discusses the numerical simulation results of swimming similar to manta rays. The complex three-dimensional kinematics of manta rays were implemented to unravel the intricacies of its propulsion mechanisms by using the discrete vortex method (DVM). The DVM replaces the requirement for a structured grid across the computational domain with a collection of vortex elements. This method simplifies grid generation, especially for intricate geometries, resulting in time and effort savings in meshing complex shapes. By modeling the pectoral fins with discrete panels and utilizing vortex rings to represent circulation and wake, the study accurately computes the pressure distribution, circulation distribution, lift coefficient, and thrust coefficient of the manta ray. This study focuses on the modulation of aerodynamic performance by altering the span length and the length change ratio during the downstroke and upstroke motion (SV). The manta ray's three-dimensional vortex configurations comprise a combination of vortex rings, vortex contrails, and horseshoe vortices. Analysis of the three-dimensional vortex structure indicates the presence of multiple vortex rings and horseshoe vortex rings at higher SV values, while adequate formation of horseshoe vortices is not observed at lower SV values. In terms of propulsive performance, both lift and thrust increase with SV, while the propulsive efficiency demonstrates its peak at SV = 1.75. The analysis reveals that at higher SV values, the net thrust generated primarily originates from the tip of the fins. Moreover, the study illustrates a significant enhancement in propulsive efficiency, particularly in association with optimal Strouhal numbers ranging between 0.3 and 0.4. The key findings of this study may be used in efficient design of agile autonomous underwater vehicles for marine exploration and surveillance applications.

The Full Non-linear Vortex Tube-Vorton Method: the pre-stall condition

The present hybrid vortex tube-vorton method is based entirely on the Full Multi-wake Vortex Lattice Method (FMVLM) concepts, which means detaching vorticity with precise vortex strength and orientation along all separation lines between each discretized element of a shell-body, including all external edges. Since the classic Vortex Particle Method (VPM) is unstable by itself because it does not conserve the total amount of circulation as time evolves (Kelvin’s circulation theorem), an isolated Vortex (regularized) Filament Method (VFM) approach is implemented to obtain advection of vorticity, while the induced velocity field is obtained through its corresponding full vorton cloud. Further, a novel vortex squeezing/stretching scheme for such a vortex cylinder-sphere approach is proposed based on variation in time for vortex volumes in order to precisely (zero residual) conserve both circulation and vorticity at each time step (for each detached vortex element), while the viscous effect can be accounted for via the Core Spreading Method (CSM).

Numerical study flow-induced vibration of four two-degree-of-freedom circular cylinders in lozenge configuration using random vortex- boundary element scheme

Flow-induced vibration around industrial structures is a significant factor contributing to the mechanical degradation of these structures exposed to fluid flow. Numerical simulation of such flows is challenging with conventional simulation methods due to the displacement of the structural boundaries and the complexity of defining and satisfying boundary conditions. In this research, the development and combination of random vortex and boundary element methods have been employed to address the aforementioned challenges. Two-dimensional flow at Reynolds numbers of 100, 200, and 1000 around four two-degrees-of-freedom circular cylinders in two lozenge configurations with different diameter ratios (parallel and vertical diameter to the flow direction) has been simulated. In configuration 1, the diameter ratio is 1.5, the horizontal and vertical diameters are equal to 3 times and 2 times the cylinder diameter, respectively. In configuration 2, the diameter ratio is 1, and the diameter of the lozenge is equal to 4 times the cylinder diameter. The changes in hydrodynamic force coefficients, and streamlines are depicted for each scenario. The oscillation amplitude of the rear cylinders, which is affected by the vortex shedding from the front cylinders, increases. In certain instances, especially at higher Reynolds numbers like Reynolds 1000, increasing in oscillation amplitude may even result in collisions between the cylinders. For configuration 2, both the average drag coefficient and the range of variation for all four cylinders are greater than those for similar cylinders in configuration 1. The results indicate that an increase in the Reynolds number from 100 to 200 and 1000 results in approximately 1.4 and 11.5 times amplification in the oscillations of the drag coefficient, and the maximum value of lift coefficient increases nearly 2.2 and 80 times, respectively.

Effect of Gating System Design on the Quality of Aluminum Alloy Castings

In this paper, a naturally pressurized gating system has been designed to reduce the turbulence of the melt during casting. The influence of gate dimensions, foam filters, a trident gate and a vortex element were evaluated. Their effect on melt velocity, flow characteristics, number of oxides, casting properties and mechanical properties were observed. ProCAST Simulation software v.2023 and a water flow test were also evaluated to assist in the experimental evaluation of the castings. Melts showed a relationship between melt velocity and porosity of castings. Quantitative evaluation of the surface porosity showed a trend of decreasing porosity with decreasing melt velocity. The greatest reduction in the melt velocity was achieved by a M4 design, which was associated with the highest reduction in the oxides. The pores analyzed proved the presence of oxide layers on their inner surface and a possible theory of pore formation when the initiator of porosity is entrained double oxide layers. The best metal yield was achieved with M1, but the difference between M2 and M4 was negligible (2–5% yield difference), so it can be stated that the beneficial effect of the M4 design in providing the best quality castings is not negated by the increase in metal yield.

Stable Vortex Particle Method Formulation for Meshless Large-Eddy Simulation

A novel formulation of the vortex particle method (VPM) is developed for large-eddy simulation (LES) in a meshless scheme that is numerically stable. A new set of VPM governing equations are derived from the LES-filtered Navier–Stokes equations. The new equations reinforce the conservation of angular momentum by resizing vortex elements subject to vortex stretching. In addition to the VPM reformulation, a new anisotropic dynamic model of subfilter-scale (SFS) vortex stretching is developed. This SFS model is well suited for turbulent flows with coherent vortical structures, where the predominant cascade mechanism is vortex stretching. The mean and fluctuating components of turbulent flow and Reynolds stresses are validated through the simulation of a turbulent round jet. The computational efficiency of the scheme is showcased in the simulation of an aircraft rotor in hover, showing our meshless LES to be 100 times faster than a mesh-based LES with similar fidelity. The implementation of our meshless LES scheme is released as open-source software, called FLOWVPM.

The Full Multi-wake Vortex Lattice Method: a detached flow model based on Potential Flow Theory

One of the main issues concerning the standard Vortex Lattice Method is its application to partially or fully detached flow conditions, where non-linear aerodynamic characteristics appear as the angle of attack increases and/or the aspect ratio decreases. In order to solve such limitations, a pure numerical approach based entirely on the Vortex Lattice Method concepts has been developed. The so-called steady “Full Multi-wake Vortex Lattice Method” comes from the main hypothesis that each discretized element on the body’s surface detaches their own wakes downstream. The obtained results match for lift, drag and moment coefficients for the entire aspect ratio range configurations (under straight wakes and inviscid assumptions). Future unsteady versions of such a multi-wake approach could improve the current results obtained through Vortex Element Methods (as vortons or isolated vortex filaments).

ACCURACY OF CALCULATIONS OF THE VELOCITY FIELD FROM THE SYSTEM OF VORTEX SEGMENTS USING GRAPHIC PROCESSORS

The paper explored the possibility of using graphics processors to calculate the velocity field from a system of vortex segments in the ideal fluid three-dimensional simulation. This study is important in view of the large number of methods that use discrete vortex structures in modeling of three-dimensional flows. When simulating numerically urban buildings by vortex methods, a huge number of vortex segments are generated. At the same time, the algorithm complexity for calculating such systems is proportional to the square of the number of elements. This requires significant computing resources, especially over a long time or with a large number of fluid-affected objects. Graphics processors have long been actively used to speed up this kind of calculations, in particular, for vortex structures modeling. However, it should be noted that the maximum simulation speed is achieved when using float type variables and this leads to an increase in calculation errors. Therefore, when using the GPU in methods where it is necessary to calculate the velocity field from a set of vortex elements, for example, point vortices in the method of discrete vortices or vortex segments in the method of discrete vortex frames, we must be sure that we do not lose the accuracy of calculations.
 Two systems of vortex segments were considered: segments located along a straight line and segments leaving the plate during flow separation. The main attention is paid to the study of the accuracy of calculations, the formation of data structures and their transfer to the graphics processor. The results indicate that the correct organization of data transfer from the central processor to the graphic processor and vice versa allows to significantly improve the speed of calculations without substantial loss of calculations accuracy.

On the pressure field, nuclei dynamics and their relation to cavitation inception in a turbulent shear layer

Cavitation inception in the turbulent shear layer developing behind a backward-facing step occurs at multiple points along quasi-streamwise vortices (QSVs), at a rate that increases with the Reynolds number (Re). This study investigates the evolution of the unsteady pressure field and the distribution of nuclei within and around the QSVs. The time-resolved volumetric velocity in the non-cavitating flow is measured using tomographic particle tracking, and the pressure is determined by spatial integration of the material acceleration. Analysis in Eulerian and Lagrangian reference frames reveals that the pressure is lower, and its minima last longer within the QSVs compared with the surrounding flow. The intermittent low pressure regions, whose sizes and shapes are consistent with those of the cavities, are likely to be preceded by axial vortex stretching and followed by contraction. Such phenomena have been observed before in simulations of stretched vortex elements. For the same axial straining, the pressure minima last longer with increasing Re, a trend elucidated in terms of viscous diffusion of the stretched vortex core. The impact of nuclei availability is studied under ‘natural’ and controlled seeding. Owing to differences in the saturation level of non-condensable gas, the microbubble concentration in the shear layer decreases with increasing Re, in contrast to the rate of cavitation events. Minor differences in entrainment rate into the shear layer also do not explain the substantial Re effects on cavitation inception. Hence, the Re scaling of inception appears to be dominated by trends of the pressure field.

Recursive computation of the multipole expansions of layer potential integrals over simplices for efficient fast multipole accelerated boundary elements

In boundary element methods (BEM) in R3, matrix elements and right hand sides are typically computed via analytical or numerical quadrature of the layer potential multiplied by some function over line, triangle and tetrahedral volume elements. When the problem size gets large, the resulting linear systems are often solved iteratively via Krylov subspace methods, with fast multipole methods (FMM) used to accelerate the matrix vector products needed. When FMM acceleration is used, most entries of the matrix never need be computed explicitly - they are only needed in terms of their contribution to the multipole expansion coefficients. We propose a new fast method - Quadrature to Expansion (Q2X) - for the analytical generation of the multipole expansion coefficients produced by the integral expressions for single and double layers on surface triangles; charge distributions over line segments and over tetrahedra in the volume; so that the overall method is well integrated into the FMM, with controlled error. The method is based on the O(1) per moment cost recursive computation of the moments. The method is developed for boundary element methods involving the Laplace Green's function in R3. The derived recursions are first compared against classical quadrature algorithms, and then integrated into FMM accelerated boundary element and vortex element methods. Numerical tests are presented and discussed.

Cavitating and Non-cavitating Lumped Vortex Element under a Free Surface

Cavitating and Non-cavitating Lumped Vortex Element under a Free Surface

Junction flow inside and around three-row cylindrical group on rigid flat surface

Groups of bluff bodies are widespread in nature and technology. These are the supports of bridge crossings, high-rise buildings in cities, offshore drilling and wind platforms, algae and vegetation in the seas and rivers, forests and other objects. The flow of air or water around such structures has a complex vortex and jet character and requires significant efforts in the process of scientific research to improve the environmental situation and reduce material and technical costs in the process of operating such structures. The purpose of the research is study the features of the generation and evolution of vortex and jet flows near and inside the three-row group of cylinders, which are installed on the rigid flat surface. The results of experimental studies showed that the flow around the group of cylinders had a complex unsteady nature, which is due to the interaction of vortex and jet flows typical flow elements with the three-row cylindrical group, which was located installed on the rigid flat surface. The three-row cylindrical group (31 piles with a diameter of 0.027 m) is a model of a bridge support, which was streamlined at a velocity of 0.06 m/s to 0.5 m/s (Reynolds number Red=(1600–6700) and Froude number Fr=(0.04–0.18)). Visual investigations and measurements of the velocity field were carried out inside and around the three-row structure. The features of the formation and evolution of vortex and jet flows inside and near the cylindrical group were established. Integral, spectral and correlation characteristics of the velocity fluctuation field were obtained. Mean, root-mean-square values of velocity and probability density functions of velocity fluctuations integrally displayed the changes in the velocity field in the spatial and temporal domain in the junction area of grillage and plate. The power spectral densities of velocity fluctuations and mutual correlation functions made it possible to study the features of the generation of the velocity fluctuation field in the frequency domain and its interrelationships in space. It was revealed that the velocity field inside the horseshoe vortex structures was multimodal. The spectral levels of velocity fluctuations at the periphery of the quasistable horseshoe vortex structures were higher than in the cores of these structures. The highest levels of the velocity fluctuation spectra were observed in front of the second lateral cylinder where the interaction of the vortex and jet flows took place. Discrete peaks in the spectral levels of velocity fluctuations are found at the frequencies of formation of large-scale wake vortices and the frequencies of formation of small-scale vortex structures of the shear layer, which are due to the Kelvin-Helmholtz instability. It has been established that the frequency of formation of shear layer vortices is (10–40) times higher than the frequency of formation of wake vortices.

A low-rank ensemble Kalman filter for elliptic observations

We propose a regularization method for ensemble Kalman filtering (EnKF) with elliptic observation operators. Commonly used EnKF regularization methods suppress state correlations at long distances. For observations described by elliptic partial differential equations, such as the pressure Poisson equation (PPE) in incompressible fluid flows, distance localization should be used cautiously, as we cannot disentangle slowly decaying physical interactions from spurious long-range correlations. This is particularly true for the PPE, in which distant vortex elements couple nonlinearly to induce pressure. Instead, these inverse problems have a low effective dimension: low-dimensional projections of the observations strongly inform a low-dimensional subspace of the state space. We derive a low-rank factorization of the Kalman gain based on the spectrum of the Jacobian of the observation operator. The identified eigenvectors generalize the source and target modes of the multipole expansion, independently of the underlying spatial distribution of the problem. Given rapid spectral decay, inference can be performed in the low-dimensional subspace spanned by the dominant eigenvectors. This low-rank EnKF is assessed on dynamical systems with Poisson observation operators, where we seek to estimate the positions and strengths of point singularities over time from potential or pressure observations. We also comment on the broader applicability of this approach to elliptic inverse problems outside the context of filtering.

Feature recognition of a 2D array vortex interferogram using a convolutional neural network

A vortex array has important applications in scenarios where multiple vortex elements with the same or different topological charges are required simultaneously. Therefore, the detection of the vortex array is vital. Here, the interferogram between the off-axis Walsh-phase plate and the vortex array is first obtained and then decoded through a convolution neural network (CNN), which can simultaneously determine the topological charge, chirality, and the initial angle. Both the theory and experiment prove that a CNN has a remarkable effect on the classification and detection of vortex arrays.

Research on smoke simulation with vortex shedding.

The Lagrangian vortex method has the advantage of producing highly detailed simulations of fluids such as turbulent smoke. However, this method has two problems: the construction of the velocity field from the vorticity field is inefficient, and handling the boundary condition is difficult. We present a pure Lagrangian vortex method, including a nested grid to accelerate the construction of the velocity field, and a novel boundary treatment method for the vorticity field. Based on a tree structure, the nested grid algorithm considerably improves the efficiency of the velocity computation while producing visual results that are comparable with the original flow. Based on the vortex-generating method, the least square method is used to compute the vorticity strength of the new vortex elements. Further, we consider the mutual influence between the generated vortex particles. We demonstrate our method’s benefits by using a vortex ring and various examples of interaction between the smoke and obstacles.

A Proper-Orthogonal-Decomposition (POD) Study of the Wake Characteristics behind a Wind Turbine Model

A comprehensive study was performed to analyze turbine wake characteristics by using a Proper-Orthogonal-Decomposition (POD) method to identify the dominant flow features from a comprehensive experimental database. The wake flow characteristics behind a typical three-bladed horizontal-axis wind turbine (HAWT) were measured in a large-scale wind tunnel with a scaled turbine model placed in a typical offshore Atmospheric Boundary Layer (ABL) wind under a neutral stability condition. A high-resolution Particle Image Velocimetry (PIV) system was used to achieve detailed flow field measurements to characterize the turbulent flows and wake vortex structures behind the turbine model. Statistically averaged measurements revealed the presence of the characteristic helical-tip vortex filament along with a unique secondary vortex filament emanating from 60% of the blade span measured from the hub. Both filaments breakup in the near-wake region (~0.6 rotor diameter downstream) to form shear layers, contrary to previous computational and experimental observations in which vortex filaments break up in the far wake. A Proper-Orthogonal-Decomposition (POD) analysis, based on both velocity and vorticity-based formulations, was used to extract the coherent flow structures, predominantly comprised of tip and midspan vortex elements. The reconstructions showed coherence in the flow field prior to the vortex breakup which subsequently degraded in the turbulent shear layer. The accuracy of the POD reconstructions was validated qualitatively by comparing the prediction results between the velocity and vorticity-based formulations as well as the phase-averaged PIV measurement results. This early vortex breakup was attributed to the reduced pitch between consecutive helical turns, the proximity between midspan filaments and blade tips as well as the turbulence intensity of the incoming boundary layer wind.

Planar potential flow on Cartesian grids

Potential flow has many applications, including the modelling of unsteady flows in aerodynamics. For these models to work efficiently, it is best to avoid Biot–Savart interactions. This work presents a grid-based treatment of potential flows in two dimensions and its use in a vortex model for simulating unsteady aerodynamic flows. For flows consisting of vortex elements, the treatment follows the vortex-in-cell approach and solves the streamfunction–vorticity Poisson equation on a Cartesian grid after transferring the circulation from the vortices onto the grid. For sources and sinks, an analogous approach can be followed using the scalar potential. The combined velocity field due to vortices, sinks and sources can then be obtained using the Helmholtz decomposition. In this work, we use several key tools that ensure the approach works on arbitrary geometries, with and without sharp edges. First, the immersed boundary projection method is used to account for bodies in the flow and the resulting body-forcing Lagrange multiplier is identified as the bound vortex sheet strength. Second, sharp edges are treated by decomposing the vortex sheet strength into a singular and non-singular part. To enforce the Kutta condition, the non-singular part can then be constrained to remove the singularity introduced by the sharp edge. These constraints and the Poisson equation are formulated as a saddle-point system and solved using the Schur complement method. The lattice Green's function is used to efficiently solve the discrete Poisson equation with unbounded boundary conditions. The method and its accuracy are demonstrated for several problems.

Accuracy of Küchemann’s prediction for the locus of aerodynamic centres on swept wings compared to an inviscid panel method

AbstractThe locus of aerodynamic centres of a finite wing is the collection of all spanwise section aerodynamic centres, and depends on aspect ratio, wing sweep and planform shape. This locus is of great importance in the positioning of vortex elements in lifting-line theory. Traditionally, these vortex elements are placed along the quarter-chord of a wing, leading to inaccurate predictions of aerodynamic coefficients for swept wings due to the discontinuity in the line of vorticity at the wing root. An analytical solution was presented by Küchemann in 1956 to determine the locus of aerodynamic centres as a function of sweep. While experimental studies have been performed to visualise this locus, no large amount of data is available to fully evaluate the accuracy of Küchemann’s analytical solution. In the present study, a numerical approach is taken using a high-order panel method for inviscid, incompressible flow to calculate the locus of aerodynamic centres for elliptic wings over a wide range of sweep angles, aspect ratios and profile thicknesses. An inviscid panel method is chosen over full CFD solutions because of their ability to isolate the inviscid phenomena. Küchemann’s prediction is compared to this numerical data. The root mean square error is calculated for each wing in a broad design space to determine the accuracy of Küchemann’s theory. It is shown to be remarkably accurate over the range of cases studied, with the root mean square error staying below 4% for all wings with aft sweep and aspect ratios higher than $R_A=5$ . The actual difference between Küchemann’s prediction and numerical data is lower than that for the majority of the span for many of the wing designs considered, with the RMS error being skewed by the results at the tip. Results demonstrate that Küchemann’s analytical equations can be used as an accurate approximation for the locus of aerodynamic centres and could be used in modern numerical lifting-line algorithms*.