Vorticity Contours Research Articles

Air Flow around and through a Permeable Semi‐Circular Cylinder‡

AbstractAn unconfined air flow across a semi‐circular permeable/porous cylinder is numerically investigated for different Reynolds (Re) and Darcy numbers (Da) at a fixed value of porosity. The Darcy‐Brinkman‐Forchheimer model has been administered to deal with the flow field inside the porous cylinder. The governing equations are solved by using the finite element method‐based commercial software COMSOL Multiphysics. The obtained flow field is analyzed by streamline profiles and vorticity contours. The collective impact of Re and Da on the drag coefficient is evaluated. At low Da values, the cylinder resembles the solid cylinder as the vorticity contours and streamlines do not infiltrate the porous media. The increment in Da leads to penetration of streamlines and vorticity contours through the porous cylinder. The drag coefficient retained an inverse relationship with Re and showed a complex relationship with Da.

V-type multigrid method in a lid-driven cavity

The study of steady incompressible viscous flow in a lid-driven cavity is done using V-type multigrid method. The second order accurate finite difference form of the Navier-Stoke’s equation is solved up to Reynolds number 10,000 using grids of maximum size 257 × 257. The validation of the result is ensured by the flow properties of primary eddy which includes the location and strength of the centres at different Reynolds numbers with the literature. Stream function, vorticity contours in the lid-driven cavity and velocity profiles at mid-section of the cavity also provide additional information for the study of flow.

Vortex particle method with iterative Brinkman penalization for simulation of flow past sharp-shape bodies

This paper presents a Lagrangian vortex method combined with iterative Brinkman penalization for the simulation of incompressible flow past a complex geometry. In the proposed algorithm, particle and penalization domains are separately introduced. The particle domain is for the computation of particle convection and diffusion, while the penalization domain is the enforcement of the wall boundary conditions. In iterative Brinkman penalization, the no-slip boundary condition is enforced by applying penalization force in multiple times within each time step. This enables large time step size reducing computational cost and maintains the capability in handling complex geometries. The method is validated for benchmark problems such as an impulsively started flow past a circular cylinder, normal to a flat plate, and a symmetric airfoil at Reynolds numbers ranging from 550 to 1000. The vorticity and streamline contours, drag, and lift coefficients show a good agreement with those reported in literature.

Heat transfer enhancement on saturated porous samples using electrostatic precipitator process in k-ε turbulent model

An influence of the electrostatic precipitator process was numerically investigated for heat transfer enhancement on saturated porous samples in a k-ε turbulent model. The condition of the water entering a test section was the inlet temperature was 30 oC (303 K), and inlet velocity was tested in the range of 1 – 2.5 m/s. The electrical voltage and time varied between 0 – 30 kV and 0 – 1 s, respectively. The initial temperature of saturated porous samples was 10 oC (283 K), and both first and second samples were set in semicircle shapes. The numerical results within the water channel showed that the electric field and electric potential zone appeared and were concentrated when using the electrostatic precipitator process. The high electric voltage could increase disturbance and turbulence within the water channel. The maximum flow field zone appeared above the saturated porous sample area, and the maximum velocity field increased with the inlet velocity and electrical voltage. The maximum pressure was increased to the high voltages, but the pressure was marginally increased with high inlet velocity. The vorticity contour for an electrostatic precipitator process was more concentrated than without the electrostatic precipitator process. Therefore, the temperature contour line in case of high inlet velocity, electrical voltage, and time can be more disturbing than the other cases. In addition, heat from the water was transferred within the sample, so the temperature within the porous sample gradually increased. The fluid velocity within the front porous sample was more within the saturated porous samples than within the porous back sample. Therefore, the flow could move through and within the samples and induce temperature within both saturated porous samples. Finally, the heat transfer within samples was enhanced by fluid flow in the water channel, so the local heat transfer coefficient within samples was induced by the fluid velocity in the water channel.

Three-dimensional flow past two stationary side-by-side circular cylinders

We conducted three-dimensional direct numerical simulations of flow past two stationary side-by-side circular cylinders. Based on the cylinder diameter, the Reynolds number was set as Re = 500 and the center-to-center spacing ratio was s/D = 1.0–5.0. In the studied parametric space, we identified five distinct flow regimes, namely, single bluff body flow at s/D = 1.1, deflected flow at s/D = 1.2–1.8, flip-flopping flow at s/D = 2.0–2.4, hybrid flow at s/D = 2.5, and antiphase flow at s/D = 2.7–5.0. The intrinsic features of each flow were elucidated using instantaneous vorticity contours, time-averaged flow fields, three-dimensional vortical structures, time histories and spectral frequencies of the drag and lift coefficients. Furthermore, the statistics of hydrodynamic forces, vortex shedding frequency, and wake three-dimensionality within each flow regime were examined thoroughly. Finally, we discussed two critical issues, namely (a) the effects of the three-dimensional vortical structures on the hydrodynamic forces and flow behaviors where both two- and three-dimensional results are compared, and (b) cylinder length effects and underlying mechanism for the switching behavior of the gap flow. We found that (1) the existence of the three-dimensional vortical structures significantly undermines the vortex interactions by absorbing energy from the spanwise vortices, and therefore, both the hydrodynamic and wake behaviors are considerably altered. (2) An increase of the cylinder length leads to the longer switching period of the gap flow in FF regime, while the transform of the gap flow direction is strongly dependent on the phase of the gap side vortices of the two cylinders.

Vortex Trapping Cavity on Airfoil: High-Order Penalized Vortex Method Numerical Simulation and Water Tunnel Experimental Investigation

This paper presents a two-dimensional implementation of the high-order penalized vortex in cell method applied to solve the flow past an airfoil with a vortex trapping cavity operating under moderate Reynolds number. The purpose of this article is to investigate the fundamentals of the vortex trapping cavity. The first part of the paper treats with the numerical implementation of the method and high-order schemes incorporated into the algorithm. Poisson, stream-velocity, advection, and diffusion equations were solved. The derivation, finite difference formulation, Lagrangian particle remeshing procedure, and accuracy tests were shown. Flow past complex geometries was possible through the penalization method. A procedure description for preparing geometry data was included. The entire methodology was tested with flow past impulsively started cylinder for three Reynolds numbers: 550, 3000, 9500. Drag coefficient, streamlines, and vorticity contours were checked against results obtained by other authors. Afterwards, simulations and experimental results are presented for a standard airfoil and those equipped with a trapping vortex cavity. Airfoil with an optimized cavity shape was tested under three angles of attack: 3°, 6°, 9°. The Reynolds number is equal to Re = 2 × 104. Apart from performing flow analysis, drag and lift coefficients for different shapes were measured to assess the effect of vortex trapping cavity on aerodynamic performance. Flow patterns were compared against ultraviolet dye visualizations obtained from the water tunnel experiment.

Aero-acoustic feedback mechanisms in supersonic cavity flow with subcavity

An open rectangular cavity with a length to depth ratio of 2 (L/D = 2) and inlet Mach number 1.71 was considered as a baseline configuration for an unsteady computational analysis. Fast Fourier transform using power spectral density, correlation, and overall sound pressure level (OASPL) was carried out on the unsteady pressure data, to analyze the flow dynamics. Many flow visualization techniques were employed such as density gradient-based numerical schlieren, vorticity contour, and streamlines for revealing major features associated with the flow. Vortex shedding visualization was carried out in terms of the Lambda 2 (λ2) criterion, where the vortex core can be observed moving downstream in the shear layer. In the acoustic pressure contours and OASPL contours, the characteristics of the acoustic waves can be distinctly observed traversing within the cavity. The analysis was extended for different flow conditions and configurations. The front wall subcavity with a ratio of subcavity length (l) to cavity length (L) l/L = 0.20 has already been established as a passive control device experimentally whereas the aft wall subcavity with l/L = 0.20 was found to behave like a passive resonator with distinct harmonic fluid-resonant modes. A more detailed investigation of these configurations with different dimensions and combinations resulted in a comparative and better understanding of the flow features, mode frequencies, and fluid-resonant oscillations in a supersonic cavity flow. Further, a method for designing front wall subcavity for passive control device has been applied to a variety of test cases and has been proven effective in suppressing the oscillations for cavity configurations with longitudinal oscillation mechanisms.

3D Structure of Striations in the North Pacific

AbstractOcean striations are composed of alternating quasi-zonal band-like flows; this kind of organized structure of currents can be found in all the world’s oceans and seas. Previous studies have mainly been focused on the mechanisms of their generation and propagation. This study uses the spatial high-pass filtering to obtain the three-dimensional structure of ocean striations in the North Pacific in both the z coordinate and σ coordinate based on 10-yr averaged Simple Ocean Data Assimilation version 3 (SODA3) data. First, we identify an ideal-fluid potential density domain where the striations are undisturbed by the surface forcing and boundary effects. Second, using the isopycnal layer analysis, we show that on isopycnal surfaces the orientations of striations nearly follow the potential vorticity (PV) contours, while in the meridional–vertical plane the central positions of striations are generally aligned with the latitude of zero gradient of the relative PV. Our analysis provides a simple dynamical interpretation and better understanding for the role of ocean striations.

Numerical Computations for Flow Patterns and Force Statistics of Three Rectangular Cylinders

In this work, numerical simulations are performed in order to study the effects of aspect ratio (AR) and Reynolds number (Re) on flow characteristics of three side-by-side rectangular cylinders for fixed spacing ratio ( g ), using the lattice Boltzmann method (LBM). The Reynolds number varies within the range 60 ≤ Re ≤ 180, aspect ratio is between 0.25 and 4, and spacing ratio is fixed at g = 1.5. The flow structure mechanism behind the cylinders is analyzed in terms of vorticity contour visualization, time-trace analysis of drag and lift coefficients, power spectrum analysis of lift coefficient and variations of mean drag coefficient, and Strouhal number. For different combinations of AR and Re, the flow is characterized into regular, irregular, and symmetric vortex shedding. In regular and symmetric vortex shedding the drag and lift coefficients vary smoothly while reverse trend occurs in irregular vortex shedding. At small AR, each cylinder experiences higher magnitude drag force as compared to intermediate and large aspect ratios. The vortex shedding frequency was found to be smaller at smaller AR and increased with increment in AR.

Meandering of a wing-tip vortex in a grid-generated turbulent flow

The interaction of a National Advisory Committee for Aeronautics 0012 wing-tip vortex with a grid-generated turbulent flow was experimentally investigated. The experiments were conducted in the near- and mid-wake regions at three free-stream turbulence (FST) levels, viz., 0.5%, 3%, and 6%, at a Reynolds number, based on the wing chord length, cw, of 2×105. Stereoscopic particle image velocimetry measurements were carried out at four downstream positions: x/cw = 1.25, 3.25, 6.25, and 7.75. Streamwise vorticity contours showed that the wing-tip vortex decayed with increased FST and downstream distance. Turbulent surroundings were found to affect the meandering amplitude of the vortex, which increased with the dispersed scatter pattern of the vortex center motion, resulting in a meandering-induced turbulence. Meandering-corrected turbulent kinetic energy revealed the existence of a laminar core at the center of the vortex surrounded by low turbulence levels outside the core. This was attributed to the stabilizing Coriolis effects of the strong rotational motion inside the vortex core, which tend to re-laminarize the turbulent fluid crossing the periphery of the vortex. Snapshot proper orthogonal decomposition analysis on the coherent component of the velocity field revealed two dominant modes forming a helical dipole, consistent with the helical displacement of a Kelvin wave with an azimuthal wavenumber |m=1|. An analysis of the terms balancing the rate of decay of the mean enstrophy revealed that increasing FST increases the stretching of the mean enstrophy within the vortex core while it reduces both its transport and convection terms. Nonetheless, the latter contributions were larger in all cases studied acting as the main mechanism for mean enstrophy decay.

Impact of Fe3O4/water on Natural Convection in Square Enclosure

Natural convection characteristics in a 2D square enclosure (10 mm x 10 mm) have been investigated detailly under natural convection conditions (103≤Gr≤105). A model has been developed to analyze the dispersed nanoparticle effect on natural convection performance in an enclosure. The left vertical wall is maintained at a high temperature, while the right vertical wall is kept at a low temperature, whereas horizontal walls are assumed to be insulated. Fe3O4/water (0≤φ≤1.0) nanofluid has been utilized to analyze the convection enhancement in the enclosure. To elucidate flow characteristics and heat transfer performance of Fe3O4/water nanofluid, temperature, velocity streamline, and vorticity contours have been taken place. It is concluded that nanoparticle dispersion in base fluid enhances the natural convection heat transfer. Also, Grashof number has an important role in heat transfer mechanism

COMPUTATIONAL FLUID DYNAMICS SIMULATION AND VISUALIZATION OF NEWTONIAN AND NON-NEWTONIAN TRANSPORT IN A PERISTALTIC MICRO-PUMP

Motivated by recent developments in bio-inspired medical engineering micro-scale pumps, in this paper, a three-dimensional sequential simulation of a peristaltic micro-pump is described to provide deeper insight into the hydromechanics of laminar, viscous flow in peristaltic propulsion. The Carreau and power-law models are employed for non-Newtonian behavior. The commercial software package ANSYS Fluent is utilized to conduct a numerical simulation of laminar peristaltic pump fluid dynamics, based on the finite volume method and steady space laminar solver. Details are provided for the geometric pump design (conducted with AUTOCAD), pre-processing (meshing) and necessary boundary conditions to simulate the peristaltic flow within the pump. Extensive visualization of velocity, pressure and vorticity contours is included. The present simulations provide a benchmark for future comparison with experimental studies and indeed more advanced numerical simulations with alternative non-Newtonian models. Applications of the study include biomimetic blood flow pumps, blood dialysis machines, micro-scale infusion pumps, etc.

The Problem of Diagnosing Jet Waveguidability in the Presence of Large-Amplitude Eddies

AbstractThe waveguidability of an upper-tropospheric zonal jet quantifies its propensity to duct Rossby waves in the zonal direction. This property has played a central role in previous attempts to explain large wave amplitudes and the subsequent occurrence of extreme weather. In these studies, waveguidability was diagnosed with the help of ray tracing arguments using the zonal average of the observed flow as the relevant background state. Here, it is argued that this method is problematic both conceptually and mathematically. The issue is investigated in the framework of the nondivergent barotropic model. This model allows the straightforward computation of an alternative “zonalized” background state, which is obtained through conservative symmetrization of potential vorticity contours and that is argued to be superior to the zonal average. Using an idealized prototypical flow configuration with large-amplitude eddies, it is shown that the two different choices for the background state yield very different results; in particular, the zonal-mean background state diagnoses a zonal waveguide, while the zonalized background state does not. This result suggests that the existence of a waveguide in the zonal-mean background state is a consequence of, rather than a precondition for, large wave amplitudes, and it would mean that the direction of causality is opposite to the usual argument. The analysis is applied to two heatwave episodes from summer 2003 and 2010, yielding essentially the same result. It is concluded that previous arguments about the role of waveguidability for extreme weather need to be carefully reevaluated to prevent misinterpretation in the future.

Solving steady-state lid-driven square cavity flows at high Reynolds numbers via a coupled improved element-free Galerkin–reduced integration penalty method

Steady-state two-dimensional lid-driven square cavity flows at high Reynolds numbers are solved in this communication using a velocity-based formulation developed in the context of the improved element-free Galerkin–reduced integration penalty method (IEFG–RIPM). The analyses based on the IEFG–RIPM are performed under a standard Galerkin weak-formulation, i.e. without the need of introducing streamline-upwind or pressure stabilizing terms in order to suppress the appearance of non-physical oscillations. Solutions in a wide range of high Reynolds numbers are successfully achieved, and the results obtained have exhibited an excellent agreement with mesh-based solutions reported in the literature. The numerical performance of the proposed IEFG–RIPM in the solution of such benchmark problem has been analysed in terms of velocity distribution, streamline patterns, vorticity and pressure contours, and also in terms of the properties of primary and secondary vortices. The outcomes of this study demonstrate the potential of the IEFG–RIPM as a feasible and reliable numerical technique for the analysis of lid-driven square cavity flows at high Reynolds numbers, allowing the fulfilment of accuracy and stability numerical requirements demanded in the solution of this benchmark problem in a remarkably simple manner.

Flow dynamics over a heated cylinder subjected to high temperature ratios

Unheated, and heated flows with forced convection over a fixed circular cylinder are studied numerically. Reynolds numbers of 80, 100, 150, and 200 are considered at different temperature ratios (T∗) of 1.66, 2.33, and 3. Different thermophysical property models of the fluid were used and implemented. The aerodynamic forces occurring on the cylinder as vortex shedding took place were explored. The drag coefficient, lift coefficient, and Strouhal number are presented and discussed. Moreover, the surface heat transfer coefficient is analyzed for the different cases of heating. It was found that increasing the temperature ratio of the cylinder caused an increase in the static load and a decrease in the dynamic load on the cylinder. In addition, the effects of cylinder surface temperature on the vorticity contours are shown for different Reynolds numbers. It was observed that increasing the temperature ratio of the cylinder caused the vortices in the wake to stretch and become weaker. This leads to total suppression of vortex shedding if sufficient heating is provided. Moreover, while the surface heat transfer coefficient of the cylinder was observed to increase with the increase of Reynolds number at constant temperature ratio, increasing the temperature ratio of the cylinder at a constant Reynolds number reduces the heat transfer coefficient and suppresses the variation in between the upper and lower sides of the cylinder.

Aerodynamic shape integrated design of wind turbine airfoils and vortex generators

ABSTRACT The current design method for wind turbine airfoils and vortex generators (VGs) is independent, which cannot be used to simultaneously design wind turbine airfoils and VGs with high aerodynamic performance. Therefore, an aerodynamic-shaped integrated design method for wind turbine airfoils and VGs is proposed. The aerodynamic-shaped VGs instead of plate VGs are introduced to be installed on wind turbine blade section. The blade airfoil and aerodynamic-shaped VGs are both expressed by B-spline function. Then, the optimal mathematic model of wind turbine airfoil with aerodynamic shaped VGs is established, for which the multi-objective functions are maximum lift to drag ratio plus maximum lift coefficient. DU97-W-300 and CLARKY-117 airfoils are selected as initial objects to be optimized simultaneously by combining CFD simulation and particle swarm optimization (PSO) algorithm. The optimal results indicate that the maximum lift coefficient and lift to drag ratio of the optimized blade with novel VGs show the increase of 9.3% and 7.5%, respectively, compared to initial design. In addition, through the comparative analysis of streamlines and vorticity contours, the new blade section with novel VGs could produce larger induced vortex and could effectively restrain the fluid separation on the blade surface. This study provides a good reference to the design and application of wind turbine airfoils and VGs.

Shock wave and turbulent boundary layer interaction in a double compression ramp

Direct numerical simulations of shock wave and supersonic turbulent boundary layer interaction in a double compression ramp with fixed ramp angles of 12o and 24o at Mach 2.9 are conducted. The characteristics of the shock interactions are investigated for four different length between the two ramp kinks, corresponding to Lc = 0.9δref, 1.8δref, 2.7δref, and 3.6δref (δref being the upstream turbulent boundary layer thickness). The influence of increasing Lc on flow structures, unsteadiness, Reynolds stress, turbulence kinetic energy, and Reynolds stress anisotropy tensor is assessed. The size of the separation region is significantly decreased and reattached flow appears between the two ramp kinks. Streamwise vorticity contours and streamline curvature show the decreased spanwise width and increased spanwise coherency of Görtler-like vortices. Analysis of fluctuating wall pressure indicates that the low-frequency unsteadiness is strongly suppressed in the interaction region. Profiles of Reynolds stress components and turbulence kinetic energy exhibit different turbulence evolution across the interaction, leading to substantial differences observed in the anisotropy invariant map. It is found that the near wall region is characterized by decreased anisotropy, becoming closer to the axisymmetric compression state, while a significant increase of turbulence is identified in the outer region, following the axisymmetric expansion limit. Moreover, downstream of the interaction, turbulence in the near-wall region experiences a faster recovery and the influence of Lc is found to be marginal. The main effect of Lc is observed in the outer region, an increase of Lc resulting in a monotonic decay of turbulence intensities and an inward movement of turbulent structures.

Hydrodynamic benefit of cephalic fins in a self-propelled flexible manta ray

The hydrodynamic benefit of cephalic fins in manta ray was explored using the penalty immersed boundary method. When manta rays feed, they open their cephalic fins and lower them to their mouth. As they swim forward, the cephalic fins are straightened in the forward direction. The smooth body of manta rays was modeled as a flexible plate. A self-propelled flexible plate was realized by enforcing a prescribed harmonic oscillation in the vertical direction but allowing the plate to move freely in the horizontal direction. Simulations without cephalic fins were also performed for comparison. Vortical structures and pressure distributions were visualized to elucidate the hydrodynamic benefits of cephalic fins. The fins generated streamwise vortices that resulted in negative pressure and enhanced the average cruising speed and thrust. The effect of the gap distance (g/L, where g is the gap distance between the two cephalic fins and L is the length of the plate) was examined in detail. The underlying propulsion mechanism was analyzed by examining the phase of the heaving stroke. The effects of the g/L were scrutinized by visualizing the contours of vorticity (ωx, ωy, ωz) and pressure (p) around the flexible plate. A maximum cruising speed was obtained at g/L = 0.6, where the average cruising speed increased by more than 62.8%.

The wake and force statistics of flow past tandem rectangles

A numerical investigation is performed to examine the effect of side ratios (SR), separation ratio (g*), and Reynolds number (Re) on the flow around tandem rectangles using the lattice Boltzmann method. The SR is set at 0.25, 0.5, 0.75 and 1. The g* is varied from 0.5 to 10. The Reynolds number is set at 75, 100, 125 and 150. The results reveal that the upstream cylinder has higher drag forces compared to the downstream cylinder. The results further show that in case of wide-wake shear layer reattachment flow, strongly interactive vortex shedding flow and weakly interactive vortex shedding flow regimes, a small increase in mean drag coefficient of upstream cylinder for all considered cases in this study is attributed to the reduction of wake width, which confirms the weakened influenced by the upstream cylinder. The results show that as the vortex shedding mostly occurs behind the downstream cylinder only, root-mean-square value of lift coefficient is a considerably larger for the downstream cylinder than for the upstream cylinder. The results further show that as the flow regime transition occurs the lift coefficients indicates either in-phase or anti-phase flow behavior. The numerical results are presented in detail in the form of vorticity contour, streamline, time history analysis of forces and vortex shedding frequencies.

Effect of axis ratio on unsteady wake of surface mounted elliptic cylinder immersed in shear flow

Three-dimensional flow past surface mounted elliptic cylinder has been investigated numerically using OpenFOAM. Axis ratio (AR) of the elliptic cylinder is varied from 0.5 to 2. Effects of shear intensity (K) of the nonuniform incoming flow and Reynolds number (Re) varying from 150 to 250 on wake dynamics have been examined using Hilbert Huang transformation and Recurrence analysis. Qualitative and quantitative analyses of wake unsteadiness are illustrated using Hilbert spectra and degree of stationarity. Various recurrence quantification estimates have been reported to reveal insight about unsteady wake transition with the change in Re, AR and K. Four types of distinguishable wake flows, viz., steady, periodic, quasi-periodic and chaotic have been characterized with the help of vorticity contours, frequency spectra and bifurcation diagram. In aperiodic flow, wake oscillation contains multiple laminar states or slow changing states which has been disclosed using laminarity and trapping time. Nonstationarity and synchronous wake behavior along the height of the cylinder have been examined using cross-recurrence analysis and quantified in terms of recurrence rate, determinism and average diagonal length. In addition, the effect of change in K for each value of Re and AR has been studied on the mean drag coefficient of the cylinder.