Vorticity Contours Research Articles

Simulation of vortex shedding around cylinders by immersed boundary-lattice Boltzmann flux solver

The hydrodynamic response accompanied with vortex shedding around circular cylinders plays a pivotal role in ocean engineering, and the numerical simulation is an essential and efficient way. The computational domain is usually in large scale for this kind of problem, and the details of flow field surrounding structures are necessary to be observed as they play key influence. Comparing with popular numerical methods for fluids such as the Navier-Stokes (N-S) solver and the lattice Boltzmann method (LBM), to some extent, the lattice Boltzmann flux solver (LBFS) inherits their advantages and removes the limitations so that the accuracy and efficiency are both ensured. In this work, the immersed boundary-lattice Boltzmann flux solver (IB-LBFS) with implicit velocity correction is implemented to simulate vortex shedding around circular cylinders. Firstly, the simulation of flow past an isolated stationary cylinder is carried out as the validation of the IB-LBFS. After that, the phenomena of flow past two stationary cylinders in two kinds of arrangements are simulated with respective spacing ratios and Reynolds numbers. The instantaneous contours of vorticity are shown to illustrate the vortex shedding, and the hydrodynamic parameters such as the drag coefficient, the lift coefficient, and the Strouhal number are given. Through comparing with previous literatures, it can be seen that the IB-LBFS is reliable and has sufficient accuracy so that it can represent the details of the flow field, for example the beat phenomenon, in this simulation, which indicates its wide application for fluid-structure interaction problems in ocean engineering.

Numerical investigations for flow past two square rods in staggered arrangement through Lattice Boltzmann method

A numerical study for two dimensional (2-D) incompressible flow past over two square rods in staggered arrangement detached with a rectangular control rod is conducted by applying single-relaxation-time lattice Boltzmann method (SRT-LBM). This study is conducted basically to reduce the fluid forces and to suppress the vortex shedding through passive control method under the effect of gap spacing between the rods and Reynolds number. The gap spacing (g = s/D) between the rods is taken as g = 1, 3 and 6 whereas, Reynolds number Re= u∞ D/γ is selected within the range of Re = 80 – 200. First validity of code and effect of computational domain along with effect of uniform inflow velocity is checked by considering upstream, downstream and height of computational domain respectively, at Lu = 7.5d, Ld = 30d and H = 14d. After that the effect of gap spacing and Reynolds number on flow structure mechanism is studied. The acquired results are obtained in terms of vorticity contour visualization, power spectrum analysis of lift coefficients and force statistics. Here, three different types of flow regimes, named as i) Irregular Single Bluff Body (ISBB), ii) Flip Flopping (FF) and iii) Anti Phase Synchronized (APS) flow regimes are observed at different values of gap spacing and Reynolds number. In study of force statistics, the values of mean drag coefficients (Cdmean), root mean square of drag coefficients (Cdrms), root mean square of lift coefficients (Clrms) and strouhal number (St) of two square rods are calculated. The values of mean drag coefficients for rod R1 is greater than that of rod R2. The Cdmean for R2 increases with increment in the values of Reynolds, while as Cdmean for R1 having mixed trend. The maximum value of Cdmean is attained at (g, Re) = (1,80) that is 1.8971 for R1 as compared to R2, where existing flow regime is the Irregular single bluff body (ISBB) flow regime. The largest value of Strouhal number is obtained for R2 at (g, Re) = (6, 150) that is 0.1608 along with Anti phase synchronized (APS) flow regime.

Suppression of vortex shedding behind a square cylinder confined in a diverging channel

Confinement can be considered as a passive method for controlling the vortex shedding behind bluff bodies. However, this technique is often accompanied with a considerable drag increase as a penalty. This paper is aimed at investigating the effects of divergence ratio (DR) from 0.2 to 1.2 on flow characteristics (instantaneous aerodynamic coefficients, time-mean drag coefficient, Strouhal number and rms value of lift coefficient) and flow topology (vorticity contour and streamlines) around a confined square cylinder at a Reynolds number of 100. Furthermore, the critical Reynolds number where the onset of vortex shedding happens is determined for all diverged channels. The results indicate that vortex shedding is completely suppressed for channels with 0.26 ≤ DR ≤ 0.45. For the channel with DR = 0.26, a drag reduction has been achieved and the drag coefficient of the square cylinder reduces by 18.85% in comparison with that of the unbounded cylinder at Re = 100. Furthermore, the critical Reynolds number which is determined to be 49 for the unconfined square cylinder is delayed to 101 in this channel. It is also found that the drag coefficient, the rms value of lift coefficient and Strouhal number increase with divergence ratio while the vortex formation length and the wake width generally decrease.

Flow transition in periodically fully developed wavy channels

In the present study, numerical investigations have been performed to study the flow transition mechanism in wavy channels using finite volume-based open source field operation and manipulation. Two different wavy channel configurations are chosen, which represent two different flow destabilization mechanisms, viz., Kelvin–Helmholtz and centrifugal instabilities. Sinusoidal walls with out-of-phase and in-phase channel configurations have been considered in the present study. Steady to chaotic flow transition in two different channel configurations are investigated by varying Reynolds number. A detailed flow regime map is presented for the two different wavy channel configurations. Unsteady flow features have been illustrated with the help of instantaneous streamlines, velocity contours, vorticity contours, and iso-Q surfaces. For the out-of-phase configuration, the flow changes from two-dimensional steady to two-dimensional unsteady in the Re range of 175–185, and then three-dimensional unsteady flow is observed for the Re varying from 250 to 260. On the contrary, for the in-phase configuration, the transition happens directly from steady two-dimensional flow (Re < 101) to unsteady three-dimensional (Re > 102) in a very narrow range of Re. Transitions in the two different wavy channels have been examined in detail using Hilbert–Huang transformation, phase-space reconstruction, Poincaré section, recurrence plot, and dynamic mode decomposition. Frequency, growth rate, and vortex structures of the dominant modes are illustrated corresponding to each value of Re for the considered channel configurations.

An experimental investigation of a rotationally oscillating cylinder

The flow patterns of the wake region of a rotationally oscillating cylinder were investigated experimentally by using the Particle Image Velocimetry (PIV) technique and dye visualization. The experiments were conducted at Reynolds number Re = 1000 and different values of oscillation amplitude (θA = 60°, 120°, 180°) and frequency ratio (FR = 0.8, 1.7, 3.3, 6.7). Dye visualizations, instantaneous vorticity contours, time-averaged streamlines, vorticity, streamwise and crossflow velocity contours, Reynolds stress correlations, turbulent kinetic energy (<TKE>) and autospectral density contours were analysed. For FR = 0.8, the vortices formation behind the cylinder wake disappeared and the only saddle point formation was observed at θA = 120° and θA = 180°. The maximum and minimum shear stress <u′v′> were obtained at FR = 0.8, θA = 180° and FR = 3.3, θA = 120°, respectively. The turbulent kinetic energy decreased with the increase in the frequency ratio at θA = 180°, and it has been observed that the vortex shedding weakens the interaction between the upper and lower vortices of the cylinder. The maximum decreasing in the drag coefficient of the stationary cylinder was by around 46% at FR = 6.7 θA = 120°. It is concluded that the rotationally oscillating cylinder has a significant effect on the cylinder wake region and changes the wake flow structures and vortex shedding patterns.

Spatio-temporal evolution of magnetohydrodynamic blood flow and heat dynamics through a porous medium in a wavy-walled artery

Background and objectiveIn a healthy body, the elastic wall of the arteries forms wave-like structures resulting from the continuous pumping of the heart. The systolic and diastolic phases generate a contraction and expansion pattern, which is mimicked in this study by considering a wavy-walled arterial structure. A numerical investigation of the spatio-temporal flow of blood and heat transfer through a porous medium under the action of magnetic field strength is conducted. MethodThe governing equations of the blood flow in the Darcy model are simulated by applying a vorticity-stream function formulation approach. The transformed dimensionless equations are further discretized using the finite difference method by developing the Peaceman-Rachford alternating direction implicit (P-R ADI) scheme. ResultsThe computational results for the axial velocity, temperature distribution, flow visualization using the streamlines and vorticity contours, isotherms, wall shear stress and the average Nusselt number are presented graphically for different values of the physical parameters. ConclusionsThe study shows that the axial velocity increases with an increase in the Darcy number, and a similar phenomenon is observed because of an amplitude variation in the wavy wall. Both temperature and wall shear stress decreases with an increase in the Darcy number. The average Nusselt number increases with the magnetic field strength, while it has a reducing tendency due to the permeability of the porous medium.

On eddy transport in the ocean. Part I: The diffusion tensor

This study provides an interpretation of isopycnal eddy transport for mass and passive tracers in double-gyre eddy-resolving oceanic circulation. This paper focuses on a transport/diffusion tensor representation of the eddy tracer flux, and a companion paper will focus on advective eddy-induced tracer and mass transports. We use a spatial filter to separate the large and small scales, which leads to results distinct from those obtained via a temporal Reynolds eddy decomposition. To work towards a parameterisation, we relate the eddy tracer flux to the large-scale tracer gradient via the transport tensor K. The symmetric part of K is the diffusion tensor, S, which parameterises diffusive fluxes and whose mixing properties are determined by the signs of its eigenvalues. The eigenvalues of S are robustly of opposite sign (polar) and thus quantify filamentation of the tracer via both up- and down-gradient fluxes. Given the prevalence of polar eigenvalues – which are also obtained for Reynolds eddy fluxes – representing their associated effects should be a target of future eddy tracer transport closures. Given the inherent inhomogeneity and anisotropy of the eddy-induced transport, we argue that a full transport tensor is better suited to this task than scalar coefficients or diagonal tensors. The diffusion axis, which represents the direction of preferential mixing, tends to align with the large-scale velocity vector and contours of large-scale relative vorticity and layer thickness. Strong shears can inhibit this alignment. We show that the large-scale velocity gradient matrix may be suitable for parameterising the transport tensor, in particular at depth. Furthermore, since entries of K and S exhibit probabilistic distributions when conditioned on certain large-scale flow features, we suggest that a stochastic closure for the eddy transport would be most suitable.

Can the ground enhance vertical force for inclined stroke plane flapping wing?

The numerical investigation of 2D insect wing kinematics in an inclined stroke plane is carried out using an immersed boundary solver. The effect of vortex shedding and dipole jet on the vertical force generation by the flapping wing due to change in the stroke plane angle is investigated in the vicinity of the ground. The results of instantaneous force and vorticity contours reveal the underlying lift enhancement mechanisms for the inclined stroke plane flapping wing. Moreover, they aid in the understanding of the wake-ground interaction and the associated shear layers. The calculated average vertical force delineates different force trends for the inclined stroke plane flapping near the ground. Furthermore, the dipole jet patterns are analyzed for different heights. These patterns are found to be a better tool to assess the kinematics for the vertical force enhancement and reduction, especially at intermediate heights. Vertical force enhancement is the critical parameter in the design of the micro aerial vehicle (MAV). Through this study, it is certain that the dipole jet has the potential to be used as a lift modification mechanism in MAVs. In summary, the study gives a holistic view of the physics of the inclined plane kinematics near the ground and serves as the basis for the design of MAVs.

Design and aerodynamic evaluation of a medium short takeoff and landing tactical transport aircraft

The present article deals with the conceptual design of a new medium short takeoff and landing tactical transport aircraft, which is intended to expand the institutional capabilities of the Colombian Air Force in terms of versatility and flexibility. An original design strategy was developed during the conceptual design, combining classical methodologies and high-fidelity computational fluid dynamics (CFD) simulations. This methodology allowed the aircraft to be assessed in a single design space, based on its design requirements, mission, and applicable airworthiness standards. Once obtained a baseline concept, the aerodynamic study focused on the flow around two types of wingtip devices: tip tanks and blended winglets. These devices were designed to optimize the performance capabilities of the aircraft, while keeping simple certification procedures. Wind tunnel experiments and CFD simulations were carried out to evaluate and select the best configuration. Lift, drag, and pitching moment coefficient charts, along with vorticity contours, are presented. Results showed that blended winglets have a significant potential for improving aircraft performance without severe structural weight penalties, allowing additional payload capabilities and/or increased range and fuel savings. Finally, the optimized aircraft is compared to major competitors in order to discuss and highlight its main advantages and feasibility for future production.

Malvinas current at 44.7°S: First assessment of velocity temporal variability from in situ data

We report current meter measurements obtained by four moorings deployed across the Malvinas Current (MC) at 44.7°S during 18 months between December 2015-June 2017. Previous measurements of the MC strength have been reported only close to the Brazil-Malvinas Confluence, hindering the interpretation of the flow variability. The record-length time averaged velocities and variance ellipses indicate a strong northward along-isobath. The MC flow is dominated by its barotropic component. The meridional velocities at the western and eastern moorings are not correlated and show large amplitude oscillations which are coherent with the passage of mesoscale features over the moorings. Satellite altimetry data, that are highly correlated with 20-day low-pass filtered in situ velocities (r ~ 0.80), show that the MC variability is affected by the propagation of sea level anomalies (SLA) along the Patagonian slope with phase speeds that range between 0.21 ± 0.04 m s−1 and 0.14 ± 0.01 m s−1. SLAs propagate northward along the slope following contours of constant planetary potential vorticity and its phase speeds decrease towards the east along the slope. SLA arriving at 44.7°S originate near the North Scotia Ridge and along the Malvinas Escarpment, along the northern edge of the Malvinas Plateau. We suggest that the interaction between mesoscale features and the complex bathymetry at those locations generate instabilities that enhance the generation of SLAs that propagate in the flow direction along the western boundary of the Argentine Basin and affect the variability of the MC velocities observed at 44.7°S.

On the Role of Bottom Pressure Torques in Wind-Driven Gyres

AbstractPrevious studies have concluded that the wind-input vorticity in ocean gyres is balanced by bottom pressure torques (BPT), when integrated over latitude bands. However, the BPT must vanish when integrated over any area enclosed by an isobath. This constraint raises ambiguities regarding the regions over which BPT should close the vorticity budget, and implies that BPT generated to balance a local wind stress curl necessitates the generation of a compensating, nonlocal BPT and thus nonlocal circulation. This study aims to clarify the role of BPT in wind-driven gyres using an idealized isopycnal model. Experiments performed with a single-signed wind stress curl in an enclosed, sloped basin reveal that BPT balances the winds only when integrated over latitude bands. Integrating over other, dynamically motivated definitions of the gyre, such as barotropic streamlines, yields a balance between wind stress curl and bottom frictional torques. This implies that bottom friction plays a nonnegligible role in structuring the gyre circulation. Nonlocal bottom pressure torques manifest in the form of along-slope pressure gradients associated with a weak basin-scale circulation, and are associated with a transition to a balance between wind stress and bottom friction around the coasts. Finally, a suite of perturbation experiments is used to investigate the dynamics of BPT. To predict the BPT, the authors extend a previous theory that describes propagation of surface pressure signals from the gyre interior toward the coast along planetary potential vorticity contours. This theory is shown to agree closely with the diagnosed contributions to the vorticity budget across the suite of model experiments.

Numerical investigation of unsteady flow across tandem square cylinders near a moving wall at Re = 100

Flow across tandem square cylinders placed close to a plane moving wall, has been studied extensively for various cylinder inter-spacing ratio (0.5≤S/D≤8) and cylinder-to-wall gap ratio values (0.1≤G/D≤4) at a fixed value of Reynolds number, Re = 100. Numerical experiments are performed using the computational package ANSYS FLUENT®. Results indicate that unsteady flow past tandem cylinders relies primarily on the presence of a moving wall. Exhaustive details on the effects of varying S/D and G/D values on the onset and suppression of vortex shedding behind the tandem cylinders are given. A detailed description of the underlying flow physics is provided through instantaneous vorticity and streamline contours. Forces such as the lift and drag acting on the cylinders are reasoned qualitatively through time-averaged pressure, lift, and drag coefficient plots. A remark on existence and suppression of flow unsteadiness is given through Strouhal number variation. A rigorous comparison of the present flow field with flow past an isolated square cylinder, square cylinder near a moving wall, and unbounded tandem cylinders is given. Overall, unlike the lift, drag coefficient values happen to be highest for single cylinder case, followed by the upstream cylinder, and they are least for the downstream cylinder.

Numerical Simulation of the Thermally Developed Pulsatile Flow of a Hybrid Nanofluid in a Constricted Channel

Heat transfer analysis of the pulsatile flow of a hybrid nanofluid through a constricted channel under the impact of a magnetic field and thermal radiation is presented. Hybrid nanofluids form a new class of nanofluids, distinguished by the thermal properties and functional utilities for improving the heat transfer rate. The behaviors of a water-based copper nanofluid and water-based copper plus a single-wall carbon nanotube, i.e., (Cu–SWCNT/water), hybrid nanofluid over each of velocity, wall shear stress, and temperature profiles, are visualized graphically. The time-dependent governing equations of the incompressible fluid flow are transformed to the vorticity-stream function formulation and solved numerically using the finite difference method. The laminar flow simulations are carried out in 2D for simplicity as the flow profiles are assumed to vary only in the 2D plane represented by the 2D Cartesian geometry. The streamlines and vorticity contours are also shown to demonstrate the flow behviour along the channel. For comparison of the flow characteristics and heat transfer rate, the impacts of variations in Hartmann number, Strouhal number, Prandtl number, and the thermal radiation parameter are analyzed. The effects of the emerging parameters on the skin friction coefficient and Nusselt number are also examined. The hybrid nanofluid is demonstrated to have better thermal characteristics than the traditional one.

Effect of Cylinder Gap Ratio on The Wake of a Circular Cylinder Enclosed by Various Perforated Shrouds

Flow over bluff bodies produces vortex shedding in their wake regions, leading to structural failure from the flow-induced forces. In this study, a passive flow control method was explored to suppress the vortex shedding from a circular cylinder that causes many problems in engineering applications. Perforated shrouds were used to control the vortex shedding of a circular cylinder at Reynolds number, Re = 200. The shrouds were of non-uniform and uniform holes with 67% porosity. The spacing gap ratio between the shroud and the cylinder was set at 1.2, 1.5, 2, and 2.2. The analysis was conducted using ANSYS Fluent using a viscous laminar model. The outcomes of the simulation of the base case were validated with existing studies. The drag coefficient, Cd, lift coefficient, Cl and the Strouhal number, St, as well as vorticity contours, velocity contours, and pressure contours were examined. Vortex shedding behind the shrouded cylinders was observed to be suppressed and delayed farther downstream with increasing gap ratio. The effect was significant for spacing ratio greater than 2.0. The effect of hole types: uniform and non-uniform holes, was also effective at these spacing ratios for the chosen Reynolds number of 200. Specifically, a spacing ratio of 1.2 enhanced further the vortex intensity and should be avoided.

Parametric Computational Assessment of Valvular Dysfunction in Discrete Subaortic Stenosis and Aortoseptal Angle Abnormalities

Objective: Discrete subaortic stenosis (DSS) is a left-ventricular outflow tract (LVOT) obstruction caused by a membranous lesion. DSS is commonly associated with steep aortoseptal angles (AoSAs) and is a major risk factor for aortic regurgitation (AR). However, the etiology of AR secondary to DSS remains poorly understood. This study aimed at quantifying computationally the mechanistic impact of AoSA steepening and DSS on aortic valve (AV) hemodynamics and AR development. Methods: A 2D LV geometry reconstructed from cine-MRI data was connected to an AV geometry to generate a unified 2D LV-AV model (Figure 1A). Six geometrical variants were considered: unobstructed (CTRL) and DSS-obstructed LVOT (DSS), each reflecting three AoSA variations (110°, 120°, 130°). (Figure 1B). Fluid-structure interaction simulations were run to compute LV blood flow, AV leaflet dynamics, and regurgitant fraction (RF). Results: AoSA steepening and DSS generated vortex dynamics alterations and stenotic flow conditions (Figure 1D). While the CTRL-110° generated the highest degree of leaflet opening asymmetry, DSS preferentially altered superior leaflet kinematics, and caused leaflet-dependent alterations in systolic fluttering. LVOT steepening and DSS subjected the leaflets to increasing WSS overloads (up to 94% increase in temporal shear magnitude), while DSS also increased WSS bidirectionality on the inferior leaflet belly (+0.30-point in oscillatory shear index) (Figure 1E). Although AoSA steepening and DSS increased diastolic transvalvular backflow, regurgitant fractions (RF<7%) remained below the threshold defining clinical mild AR. Conclusions: The mechanical interactions between AV leaflets and LVOT steepening/DSS hemodynamic derangements do not cause AR. However, the leaflet WSS abnormalities predicted in those anatomies provide new support to a mechanobiological etiology of AR secondary to DSS. Figure 1. Unified 2D LV-AV FSI simulations in unobstructed (CTRL) and obstructed (DSS) LVOT anatomies: A) schematic showing the LV-AV assembly, B) LVOT geometries in considered in this study, C) AV geometry with WSS characterization sites, D) snapshots of velocity vector and vorticity contour fields taken at peak systole, E) 3D surface plots regional showing time-averaged WSS characteristics for all models

Numerical Investigation of Interference Effects of Two Rectangular Tall Buildings on Aerodynamic Response

In this numerical investigation, the effect of upstream and downstream interference of two identical tall buildings was evaluated using the computational wind engineering (CWE) method. In order to simulate three-dimensional turbulent wind flow with Reynolds numbers in the range of 1.4×〖10〗^4<Re<8×〖10〗^4, the Large Eddy Simulation (LES) model was used. Mean and fluctuating coefficients of drag and lift and pressure distribution were used as the main criteria to evaluate the aerodynamic response of the principal building in different conditions of interference. Streamlines and vorticity contours were presented and their relationship to aerodynamic results was interpreted to provide a better understanding of the physics of the problem. According to the results, the shielding effect of the interfering building in most interference cases led to a reduction of the mean drag coefficient of the principal building compared to the isolated case. Compared to the isolated building, depending on the location of the interfering building, the fluctuating lift coefficient either increases or decreases.Upstream interfering buildings with sufficient distance to the principal building lead to an increase in the fluctuating lift coefficient of approximately about 50 percent. While, the fluctuating lift coefficient of the principal building decreases up to 37 percent, due to the closely spaced tandem interference states. While the mean pressure coefficient at the windward surface is not significantly sensitive to the interference states, it is strongly influenced by the different states of the interference at the lateral and leeward surfaces. Aerodynamic parameters were less sensitive to Reynolds number variations due to the fixed position of the flow separation in the sharp corners of the rectangular section and the zero angle of attack in this study. Changes in the Reynolds number resulted in variations of about 4 to 10% in the drag and lift coefficients of the principal building.

Vortex-induced vibration of a cylinder with nonlinear energy sink (NES) at low Reynolds number

Vortex-induced vibration (VIV) is a fluid structure interaction phenomena that can lead to the fatigue failure of high-rise structures. To study the basic principles and method of VIV suppression for a cylinder structure, a two-dimensional simulation model using a cylinder with two degrees of freedom in-line and cross-flow directions is presented herewith. A nonlinear energy sink is added to cylinder structures to assess its impact on vibration suppression. As a result, this study aims to investigate the VIV of cylinder under the action of the NES at low Reynolds numbers. The accuracy of the simulation model is verified by the comparison with the experimental results. Particularly, the VIV response is investigated with different mass ratio $$\beta$$ between the NES and cylinder (namely $$\beta$$ of 0.15, 0.2 and 0.3) at Re = 100 in air environment by analyzing the vibration response, phase diagram, time–frequency and vorticity contours of cylinder and NES oscillator. Three distinct function modes of NES for selected mass ratio $$\beta$$ are also observed. The results indicate that the NES can change between resonance capture states, from weak to strong, when the mass ratio $$\beta$$ increases to a defined value. In this case, the main vibration frequency of the cylinder varies over time, and the motion is in the chaotic state. The NES can also effectively reduce the vibration amplitude in both the in-flow and cross-flow directions.

Non-Newtonian power-law fluid flow over obstacles embedded inside a cavity

In this study, the flow of non-Newtonian fluid inside the lid-driven cavity with obstacle(s) is examined. The behavior of the fluid is described by the Ostwald-de Waele or power-law model. The lattice Boltzmann method (LBM) with a multiple-relaxation-time (MRT) collision model is employed to simulate complex fluid flows around the circular and square obstacles embedded inside a cavity. The stability of the present MRT-LBM algorithm in terms of so-called, cell-Reynolds number is investigated. The physics of flow structure and examinations of streamlines and vorticity contours are carried out for power-law as well as Newtonian fluids. For a single obstacle, the effects of various parameters such as Reynolds number (with respect to lid-dimension), obstacle size, power-law index, and shape of the obstacle on the flow characteristics and vortex formation are investigated. Furthermore, the effect of two square obstacles arranged in side-by-side and tandem manners inside the cavity is analyzed. Finally, the complex fluid flow over the multiple square obstacles embedded inside the cavity as a porous block for two blockage ratios is examined.

Fluid–structure coupling in time domain for dynamic stall using purely Lagrangian vortex method

This paper presents the purely fast Lagrangian vortex method (FLVM) for the simulation of the external incompressible flows past heaving and pitching bodies with high-frequency oscillation. The Nascent vortex element is introduced to the flow field to retain the Lagrangian characteristics of the solver. The viscous effect is modeled using a core spreading method coupled with the splitting and merging spatial adaptation scheme. The particle’s velocity is calculated using Biot–Savart formulation. To accelerate computation, a fast multipole method (FMM) is employed. The validity of FLVM solver is verified by temporal and spatial convergence studies for the case of flows past an impulsively started cylinder at the Reynolds numbers ranging from 50 to 9500. The accuracy of FLVM is then confirmed for the simulation of flows around the pitching flat plate and oscillating airfoil. The time history of drag and lift coefficients and the vorticity contours show a good agreement with those reported in literature. Furthermore, the FLVM is employed to determine the flutter derivatives and flutter speed of an oscillating flat plate. Results are compared with theoretical solutions based on Theodorsen’s function. In general, the results agree well with those obtained by the inviscid theory.

Influence of Blade Tip Surface Roughness on the Performance of a Single-Stage Axial Flow Compressor

Abstract Numerical investigations are carried out in a single-stage subsonic axial flow compressor to unravel the influence of blade tip surface roughness on the tip leakage flow characteristics and hence the compressor performance. The studies were carried out at different tip clearance of 0.38τ, 0.77τ, 1.15τ, and 1.54τ and blade tip surface roughness of 0.31ε and 0.62ε. The tip clearance of 0.38τ with blade tip surface roughness of 0.62ε resulted in the highest stall margin and pressure rise of 20.3% and 4.3%, respectively. The compressor blade loading was found to be improved by 5.9% after incorporating the blade tip surface roughness. The isosurfaces of vorticity contour plotted using the Q-criterion showed the reduction in strength of the tip leakage vortex. The tip leakage trajectory was found to be shifted toward the suction surface of the blade for the blade tip with surface roughness. This positive alteration in the tip leakage flow structure led to the improved performance for the blade tip with surface roughness.