Terms Of Vorticity Research Articles

CFD investigation of blind-tee effects on flow mixing mechanism in subsea pipelines

ABSTRACT Blind tees are widely used in subsea pipelines to enhance the mixing conditions of oil and gas products, but their structural design still relies on experience. In this paper, a series of numerical investigations have been carried out on blind-tee pipes in order to develop an in-depth understanding of their mixing mechanism and clarify the effects of blind-tee structures on the pipe flow. Firstly, the three-dimensional flow conditions in a typical blind tee have been simulated under different Reynolds numbers to investigate the mixing mechanism. Two critical Reynolds numbers for the vortex generations in blind tees are determined in the laminar flow regime, and the fitting curves of blind-tee vorticity dissipations are obtained. Then, the geometrical parameters, including the radial size ϕ, axial length (BSL) and position of the blind section, are varied systematically to study their effects on the flow characteristics and mixing conditions. The results indicate that increasing ϕ and BSL in an appropriate range can strengthen the flow circulation and promote the fluid exchange. Finally, an optimal configuration is obtained, which can improve the mixing capacity of blind tee by 53% in terms of the volume average vorticity as compared to the typical structure.

Pore-scale numerical simulations of flow and convective heat transfer in a porous woven metal mesh

• The fluid dynamics through the woven mesh were studied from the pore scale. • The numerical model was verified in comparison with experimental data. • The flow patterns inside the pores of the woven mesh were studied in detail. • Difference between the numerical and the analytical results of friction factor is 5%. • A new correlation of the Nusselt number was proposed. Woven metal meshes have received considerable attention in several engineering applications owing to their excellent physical properties. Macroscopic parameters, such as flow resistance and heat transfer coefficient through the porous structure, have been extensively investigated. However, the microscale mechanism requires further analysis. In this study, a numerical model was developed to evaluate the fluid dynamics and heat transfer characteristics of a porous woven mesh at the pore scale. The accuracy of the model was verified by comparing the simulated results with experimental data. Flow patterns were comprehensively studied in terms of velocity, helicity, and vorticity. The effects of the fluid properties on the flow behavior were examined. The flow reversal region downstream of the mesh expanded as the Reynolds number increased. Based on the pore-scale numerical results, a Nusselt number correlation was derived for convective heat transfer in the porous woven mesh. This study provides insights into the flow physics within a woven mesh and a framework to optimally design related devices.

Effect of thermal shear on longitudinal spin polarization in a thermal model

By including the recently introduced thermal shear term that contributes to the spin-polarization vector at local equilibrium, we determine longitudinal polarization of $\mathrm{\ensuremath{\Lambda}}$ hyperons emitted from a hot and rotating hadronic medium using the thermal model with single freeze-out. In our analysis, we consider the RHIC top energies and use the model parameters which were determined in the earlier analyses of particle spectra and elliptic flow. We confirm that, unlike the previous calculations done by using only the thermal vorticity, the thermal shear term alone leads to the correct sign of the quadrupole structure of the longitudinal component of the polarization three-vector measured in experiments. However, we find almost complete cancellation between thermal shear and vorticity terms, which eventually leads to disagreement with the data. To clarify the role played by velocity and temperature gradient terms, we present a systematic analysis of different contributions to the longitudinal polarization. Finally, replacing the mass of $\mathrm{\ensuremath{\Lambda}}$ hyperon with its constituent strange quark mass in the polarization formula we achieve agreement with the data.

Deterministic Model of the Eddy Dynamics for a Midlatitude Ocean Model

AbstractMesoscale eddies, although being on scales ofO(20–100) km, have a disproportionate role in shaping the mean stratification, which varies on the scale ofO(1000) km. With the increase in computational power, we are now able to partially resolve the eddies in basin-scale and global ocean simulations, a model resolution often referred to as mesoscale permitting. It is well known, however, that due to gridscale numerical viscosity, mesoscale-permitting simulations have less energetic eddies and consequently weaker eddy feedback onto the mean flow. In this study, we run a quasigeostrophic model at mesoscale-resolving resolution in a double gyre configuration and formulate a deterministic closure for the eddy rectification term of potential vorticity (PV), namely, the eddy PV flux divergence. Our closure successfully reproduces the spatial patterns and magnitude of eddy kinetic and potential energy diagnosed from the mesoscale-resolving model. One novel point about our approach is that we account for nonlocal eddy feedbacks onto the mean flow by solving the “subgrid” eddy PV equation prognostically in addition to the mean PV.

Comparing steady and unsteady rectangular jets issuing into a crossflow

The foundational differences of steady and unsteady jets issued into a laminar boundary layer crossflow are considered. Jets have been used widely for flow control applications, due to their ability to enhance mixing and mitigate separation, but it is unclear what role jet steadiness plays in flow control effectiveness. Here we compare experimentally unsteady (synthetic) and steady rectangular jets issued into a flat-plate laminar boundary layer with varying orifice pitch and skew. The coherent streamwise vortices produced by unsteady jets were shown to be much stronger than those produced by steady jets, despite producing similar flow patterns. These differences are rooted in how vorticity is generated in the orifice, through either a Stokes layer (unsteady) or a Blasius boundary layer (steady). Exploring the time- and phase-averaged vorticity transport equation reveals that the time-varying vorticity term is the reason for the enhanced vortical structure. When considering flow control metrics, we find that the unsteady jet produced greater added momentum in the boundary layer and added vorticity when compared to a momentum-matched steady jet. Both the steady and unsteady jets produced similar jet penetration characteristics.

Existence of solutions for nonlinear elliptic equations modeling the steady flow of the antarctic circumpolar current

In this paper, we study the steady and purely azimuthal flow model representing the Antarctic Circumpolar Current, which is described as a semi-linear elliptic equation. By means of the Mercator projection, the mathematical model is transferred into a second order elliptic equation. We give sufficient conditions to guarantee the existence of solutions for this second elliptic equation with two forms of nonlinear ocean vorticity term.

Aeroacoustic Simulation of an Owl Wing Cross-section Using Computational Fluid Dynamics

In this study, we aim to investigate the low noise flights of owls in terms of aerodynamics. The flow around cross-section of an owl wing, which is known for its nearly silent flight, is numerically analyzed using Computational Fluid Dynamics (CFD). The analysis are based on the parameters of angle of attack and the flight speed. The aerodynamic effects on the acoustic is compared in terms of vorticity and sound pressure level, where the frequency interval for the acoustic data is set to 0-7500Hz. It was seen that the vortical organisations around the airfoils are closely related to the acoustic results. The results show that the increase in both velocity and angle of attack affect the vorticity, thus lead to a rise in sound pressure level. It can be stated that the owl airfoil shape ensures a relatively silent flight.

Experimental investigation on the water hammer characteristic of stalling fluid in eccentric casing-tubing annulus

This study aims to analyze the water hammer characteristics of water hammer on tubing offset center in oil project for providing reference for water injection and well washing. An analysis is conducted by utilizing a test apparatus, particle image velocimetry, and a transient pressure measurement system. The characteristic of dynamic fluid loss is investigated in eccentric annulus flow channel and tubing and in flow line in terms of velocity, vorticity, and pressure field. Results show that water hammer occurs, and the pressure of oil casing annulus increases at the inside and outside walls with the increase in eccentricity. The water hammer pressure forms double imbalance in the internal and external walls of eccentric annulus tubing. With the increase in eccentricity, flow velocity decreases in the small flow passage, and flow velocity attenuation is fast at oil casing annulus.

Global Λ polarization in heavy-ion collisions at energies 2.4–7.7 GeV: Effect of meson-field interaction

Based on the three-fluid model, the global $\mathrm{\ensuremath{\Lambda}}$ polarization in $\mathrm{Au}+\mathrm{Au}$ collisions at 2.4 $\ensuremath{\le}\sqrt{{s}_{NN}}\ensuremath{\le}$ 7.7 GeV is calculated, including its rapidity and centrality dependence. Contributions from the thermal vorticity and meson-field term (proposed by Csernai, Kapusta, and Welle) to the global polarization are considered. The results are compared with data from recent and ongoing STAR and HADES experiments. It is predicted that the polarization maximum is reached at $\sqrt{{s}_{NN}}\ensuremath{\approx}3$ GeV, if the measurements are performed with the same acceptance. The value of the polarization is very sensitive to interplay of the aforementioned contributions. In particular, the thermal vorticity results in quite strong increase of the polarization from the midrapidity to forward/backward rapidities, while the meson-field contribution considerably flattens the rapidity dependence. The polarization turns out to be very sensitive to details of the equation of state. While collision dynamics become less equilibrium with decreasing collision energy, the present approach to polarization is based on the assumption of thermal equilibrium. It is found that equilibrium is achieved at the freeze-out stage, but this equilibration takes longer at moderately relativistic energies.

Reexamination of local spin polarization beyond global equilibrium in relativistic heavy ion collisions

We study local spin polarization in the relativistic hydrodynamic model. Generalizing the Wigner functions previously obtained from chiral kinetic theory by Y. Hidaka et al. [Phys. Rev. D 97, 016004 (2018)] to the massive case, we present the possible contributions up to the order of $\hbar$ from thermal vorticity, shear viscous tensor, other terms associated with the temperature and chemical-potential gradients, and electromagnetic fields to the local spin polarization. We then implement the (3+1)-dimensional viscous hydrodynamic model to study the spin polarizations from these sources with a small chemical potential and ignorance of electromagnetic fields by adopting an equation of state different from those in other recent studies. Although the shear correction alone upon the local polarization results in a sign and azimuthal-angle dependence more consistent with experimental observations, as also discovered in other recent studies, it is mostly suppressed by the contributions from thermal vorticity and other terms that yield an opposite trend. It is found that the total local spin polarization can be very sensitive to the equation of states, the ratio of shear viscosity to entropy density, and the freeze-out temperature.

JOANNE: Joint dropsonde Observations of the Atmosphere in tropical North atlaNtic meso-scale Environments

Abstract. As part of the EUREC4A field campaign which took place over the tropical North Atlantic during January–February 2020, 1215 dropsondes from the HALO and WP-3D aircraft were deployed through 26 flights to characterize the thermodynamic and dynamic environment of clouds in the trade-wind regions. We present JOANNE (Joint dropsonde Observations of the Atmosphere in tropical North atlaNtic meso-scale Environments), the dataset that contains these dropsonde measurements and the products derived from them. Along with the raw measurement profiles and basic post-processing of pressure, temperature, relative humidity and horizontal winds, the dataset also includes a homogenized and gridded dataset with 10 m vertical spacing. The gridded data are used as a basis for deriving diagnostics of the area-averaged mesoscale circulation properties such as divergence, vorticity, vertical velocity and gradient terms, making use of sondes dropped at regular intervals along a circular flight path. A total of 85 such circles, ∼ 222 km in diameter, were flown during EUREC4A. We describe the sampling strategy for dropsonde measurements during EUREC4A, the quality control for the data, the methods of estimation of additional products from the measurements and the different post-processed levels of the dataset. The dataset is publicly available (https://doi.org/10.25326/246, George et al., 2021b) as is the software used to create it (https://doi.org/10.5281/zenodo.4746312, George, 2021).

New governing equations for fluid dynamics

The difference in the governing equation between inviscid and viscous flows is the introduction of viscous terms. Traditional Navier–Stokes (NS) equations define stress based on Stokes’s assumptions. In NS equations, stress is supposedly proportional to strain, and both strain and stress tensors are symmetric. There are several questions with NS equations, which include the following: 1. Both symmetric shear terms and stretching terms in strain and stress are coordinate-dependent and thus not Galilean invariant. 2. The physical meaning of both diagonal and off-diagonal elements is not clear, which is coordinate-dependent. 3. It is hard to measure strain and stress quantitatively, and viscosity is really measured by vorticity, not by symmetric strain. 4. There is no vorticity tensor in NS equations, which plays an important role in fluid flow, especially for turbulent flow. The newly proposed governing equations for fluid dynamics use the vorticity tensor only, which is anti-symmetric. The advantages include the following: 1. Both shear and stress are anti-symmetric, which are Galilean invariants and independent of coordinate rotation. 2. The physical meaning of off-diagonal elements is clear, which is anti-symmetric shear stress. 3. Viscosity coefficients are obtained by experiments, which use vorticity. 4. The vorticity term can be further decomposed into rigid rotation and anti-symmetric shear, which are important to turbulence research. 5. The computation cost for the viscous term is reduced to half as the diagonal terms are all zero and six elements are reduced to three. Several computational examples are tested, which clearly demonstrate both NS and new governing equations have exactly the same results. As shown below, the new governing equation is identical to NS equations in mathematics, but the new one has lower cost and the several advantages mentioned above, including the possibility to study turbulent flow better. It is recommended to use the new governing equation instead of NS equations. The unique definition and operation of vectors and tensors by matrix and matrix operation are also discussed in this paper.

Evolution of IMD’s operational extended range forecast system of tropical cyclogenesis over North Indian Ocean during 2010-2020

The post monsoon seasons (October-December; OND) are known to produce tropical cyclones (TCs) of severe intensity over the North Indian Ocean (NIO) and particularly over the Bay of Bengal (BoB). The evolution of operational extended range forecast (ERF) of cyclogenesis probability during 2010 to 2020 based on dynamical models have been discussed. The ERF of cyclogenesis probability based on ECMWF and CFSv1 dynamical models had a modest beginning in 2010 with reasonable performance in case of severe cyclonic storm ‘Jal’ formed during the first week of November. The 2015 cyclone season with active Arabian Sea and inactive BoB was also very well captured in the real time ERF. IMD implemented CFSv2 coupled model for operational ERF in 2017 and based on it the Genesis Potential Parameter (GPP) is calculated for four weeks by using the dynamical variables like vorticity, divergence, vertical wind shear & mid-level relative humidity and was tested for the ‘Ockhi’ cyclone of 24-30 November, 2017. The GPP in case of ‘Ockhi’ cyclone was well predicted in the ERF, however, with a lead time of only one week. The Improved GPP (IGPP) is used since 2019, which can be applied both over the Ocean and the land region. In the case of IGPP the vorticity and middle tropospheric humidity terms of GPP have been retained but the thermodynamic term is modified as the scaled and averaged equivalent potential temperature between 1000 and 500 hPa. The vertical shear between 850 and 200 hPa is scaled and averaged over an annular region between 100 and 200 km radii for each grid point. In case of Super cyclone “Amphan” it indicated the genesis of the system in “Week 1” and “Week 2” forecast and also its re-curvature northeastward like the observed track. The cyclone “Nisarga” over the Arabian Sea and its track towards western coast of India was well captured in week 1 forecast based on Initial Condition of 27 May, 2020. The IGPP also showed reasonable skill in ERF in predicting the genesis of three intense cyclones viz., ‘Gati’ during 21-24 November, ‘Nivar’ during 22-26 November and ‘Burehi’ during 30 November to 5 December and the two depressions of October, 2020. Considering the significant role of Madden Julian Oscillation (MJO) in BoB TC genesis, IMD is making use of the operational IGPP along with other parameters like current and forecast MJO, Tropical Cyclone Heat Potential etc and the value-added cyclogenesis probability outlook is being issued for two weeks on every Thursday.

Velocity-vorticity-pressure formulation for the Oseen problem with variable viscosity

We propose and analyse an augmented mixed finite element method for the Oseen equations written in terms of velocity, vorticity, and pressure with non-constant viscosity and homogeneous Dirichlet boundary condition for the velocity. The weak formulation includes least-squares terms arising from the constitutive equation and from the incompressibility condition, and we show that it satisfies the hypotheses of the Babu\vska-Brezzi theory. Repeating the arguments of the continuous analysis, the stability and solvability of the discrete problem are established. The method is suited for any Stokes inf-sup stable finite element pair for velocity and pressure, while for vorticity any generic discrete space (of arbitrary order) can be used. A priori and a posteriori error estimates are derived using two specific families of discrete subspaces. Finally, we provide a set of numerical tests illustrating the behaviour of the scheme, verifying the theoretical convergence rates, and showing the performance of the adaptive algorithm guided by residual a posteriori error estimation.

Vorticity transports in turbulent channels under large-scale control via spanwise wall jet forcing

Vorticity transport in turbulent channels under large-scale active drag control (i.e., spanwise opposed jet forcing) is investigated via direct numerical simulation of the Navier–Stokes equation. The skin-friction coefficient is newly expressed by the volume integration average of the mean flow dissipation expressed in terms of the spanwise vorticity (Ωz), and the turbulent transports of the spanwsie vorticity fluctuation (−v′ω′z) and of the wall-normal vorticity fluctuation (w′ω′y). Three Reynolds number cases (i.e., Reτ=180,395, and 550) with notable drag reductions (i.e., 18%, 16%, and 15%, respectively) are examined, following the setup in Yao et al. [Phys. Rev. Fluids 2, 062601(R) (2017)]. The transports of vorticity fluctuations dominate the contributions to the frictional drag, consistent with previous results for the passive drag reduction strategy of slip-wall [Yoon et al., Phys. Fluids. 28, 081702 (2016)]. Specifically, the effect of −v′ω′z is to increase drag (due to sweeping −v′), while w′ω′y decreases the drag. A triple decomposition (mean, coherent, and random) reveals the random −v″ω′′z as the only term adding to drag, while the random w″ω′′y and the coherent −ṽω̃z and w̃ω̃y transports all decrease the drag. Weighted joint probability distribution function (p.d.f.) of v″ and ω′′z shows a transition from the first–third quadrant dominance (hence positive-correlated) near the wall to the second–fourth quadrant dominance (hence negative-correlated) away from wall. In contrast, w″ and ω′′y are negatively correlated in the entire region. The analysis here suggests that the suppression of random spanwise-vorticity transport (v″ω′′z) is the target for more effective drag reduction under the current method.

Error analysis for a vorticity/Bernoulli pressure formulation for the Oseen equations

Abstract A variational formulation is analysed for the Oseen equations written in terms of vorticity and Bernoulli pressure. The velocity is fully decoupled using the momentum balance equation, and it is later recovered by a post-process. A finite element method is also proposed, consisting in equal-order Nédélec finite elements and piecewise continuous polynomials for the vorticity and the Bernoulli pressure, respectively. The a priori error analysis is carried out in the L2-norm for vorticity, pressure, and velocity; under a smallness assumption either on the convecting velocity, or on the mesh parameter. Furthermore, an a posteriori error estimator is designed and its robustness and efficiency are studied using weighted norms. Finally, a set of numerical examples in 2D and 3D is given, where the error indicator serves to guide adaptive mesh refinement. These tests illustrate the behaviour of the new formulation in typical flow conditions, and also confirm the theoretical findings.

Lattice Boltzmann analysis of fluid structure interaction mechanism around a row of five side-by-side square cylinders

In this paper numerical investigations are performed to examine the effect of Reynolds numbers (Re) and spacing ratios (g) on flow around a row of five side-by-side square cylinders using the lattice Boltzmann method. The Reynolds number is varied in the range 75 ≤ Re ≤ 175, while spacing ratio is varied between 0.5 and 5. The flow structure mechanism around a row of five side-by-side square cylinders is studied in terms of vorticity contours visualization, time trace analysis of drag and lifts coefficients, and power spectrum analysis of lift coefficient. The effect of Re on force statistics like mean drag coefficient and Strouhal number is also analyzed. The present data are compared with the data of single square cylinder and good agreement is observed for large spacing ratio (g = 5). The flow behind five side-by-side square cylinders is classified into three different flow regimes and these regimes are further subdivided into seven different regimes. The observed flow regimes are compared with those of the other researchers published studies and found good agreement.

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.

Diagnostic study of diabatic heating and potential vorticity during a case of cyclogenesis

On 16-17 November, 2015, north and middle regions of Saudi Arabia were hit by a case of cyclogenesisassociated with heavy rainfall. This work presents a diagnostic study of this heavy rainfallcase based on the analysis of diabatic heating and potential vorticity. The synoptic analysis investigate that the important dynamical factors that causes this case are the northward extension of Red Sea Trough, anticyclone over the Arabian Peninsula, a travailing midlatitude upper trough, moisture transport pathways and strong upward motion arising from tropospheric instability. The calculation of diabatic heating by the thermodynamic equation illustrate that the contribution of vertical temperature advection and the adiabatic term are opposite to each other during the period of study. The largest contribution of the horizontal cold advection occurs during the first two days while the largest contribution of the horizontal warm advection occurs during the maximum development days. The dynamics of the studied case are also investigated in terms of isobaric Potential Vorticity. It is found that the location of the low-level Potential Vorticity anomaly and the Potential Vorticity generation estimates coincides with the heating region, which implies that condensation supports a large enough source to explain the existence of the low-level Potential Vorticity anomaly.

Pulsatile flow dynamics in symmetric and asymmetric bifurcating vessels

Bifurcating vessel is a characteristic feature of biological systems such as arteries in the cardiovascular system and pulmonary airways. In cardiovascular system, the bifurcations are often asymmetric, flow is pulsatile, and the fluid, blood, shows a complex rheology. In this work, we study computationally pulsatile flow in planar symmetric and asymmetric, three-dimensional bifurcating vessels. The fluid is considered to be Newtonian as well as non-Newtonian following Carreau's model, and the results are compared. While the flow divides in the two daughter tubes equally in symmetric bifurcations, the flow distribution is time-dependent during a cardiac cycle in asymmetric bifurcations. The flow pattern changes significantly during a cardiac cycle. The secondary flow caused by a turning streamline is analyzed in terms of secondary velocity, vorticity, and helicity. Significant variation is observed in the secondary flow in a cardiac cycle. The secondary flow is observed to be stronger at the start of the diastole despite reduced flow rate. The separated flow on the outer wall causes a significant reduction in time-averaged wall shear stress, a biomarker to assess the possibility of atherosclerotic plaque development. While no significant difference is observed in the results obtained for Newtonian and non-Newtonian fluids at high shear rates, for example, during systole, significant differences are observed when the shear rate is low, during diastole or in the separation region. The velocity profile for the non-Newtonian fluid is observed to be flatter than that for Newtonian fluid. Further oscillatory shearing index, relative residence time, the parameters used as biomarkers are presented.