Terms Of Vorticity Research Articles

Natural convection of CNT-water nanofluid in an annular space between confocal elliptic cylinders with constant heat flux on inner wall

In this paper, free convection heat transfer in an annulus between confocal elliptic cylinders filled with CNT-water nanofluid is investigated numerically. The inner cylinder is at constant surface heat flux while the outer wall is isothermally cooled. Equations of continuity, momentum and energy are formulated using the dimensionless form in elliptic coordinates for two-dimensional, laminar and incompressible flow under steady state condition, which is expressed in terms of vorticity and stream function. The governing equations are discretized using the control volume method. For the thermo-physical properties of CNTs, empirical correlations are used in terms of the volume fraction of nanoparticles. For the effective thermal conductivity of CNTs, a new model has been used. The study is performed for modified Rayleigh number (103≤ Ram ≤106), volume fraction of nanoparticles (0≤ f ≤0.12). The eccentricity of the inner and outer ellipses and the angle of orientation are fixed at 0.9, 0.6 and 0°, respectively. Results are presented in the form of streamlines, isotherm contours, and distribution of temperature and local and average Nusselt numbers on solid boundaries. The results are also discussed in detail and a very good agreement exists between the present results and those from the literature.

Bottom-topography effect on the instability of flows around a circular island

Instabilities of a two-dimensional quasigeostrophic circular flow around a rigid circular wall (island) with radial offshore bottom slope are studied analytically. The basic flow is composed of two concentric, uniform potential-vorticity (PV) rings with zero net vorticity attached to the island. Linear stability analysis for perturbations in the form of azimuthal modes leads to a transcendental eigenvalue equation. The non-dimensional governing parameters are beta (associated with the steepness of the bottom slope, hence taken to be negative), the PV in the inner ring and the radii of the inner and outer rings. This setting up of the problem allows us to derive analytically the eigenvalue equation. We first analyse this equation for weak slopes to understand the asymptotic first-order corrections to the flat-bottom case. For azimuthal modes 1 and 2, it is found that the conical topographic beta effect stabilizes the counterclockwise flows, but destabilizes clockwise flows. For a clockwise flow, the beta effect gives rise to the mode-1 instability, contrary to the flat-bottom case where this mode is always stable. Moreover, however small the slope steepness (beta) is, it leads to the mode-1 instability in a large region in the parameter space. For steep slopes, the beta term in the PV expression may dominate the relative vorticity term, causing stabilization of the flow, as compared to the flat-bottom case, for both directions of the basic flow. When the flow is counterclockwise and the slope steepness is increased, mode 2 turns out to be entirely stable and modes 3, 4 and 5 enlarge their stability regions. In a clockwise flow, when the slope steepness is increased, mode 1 regains its stability in the entire parameter space, and mode 2 becomes more stable than mode 3. The bifurcation of mode 1 from stability to instability is discussed in terms of the Rossby waves at the contours of discontinuity of the basic PV and outside the uniform-PV rings.

Unsteady MHD mixed convection flow in a lid-driven cavity with a heated wavy wall

The unsteady mixed convection flow under the effect of an externally applied uniform magnetic field is investigated numerically in a lid-driven cavity with a sinusoidal wavy wall. The governing equations given in terms of stream function, vorticity and temperature are discretized by using the dual reciprocity boundary element method (DRBEM) in space and a two-level time integration scheme is employed in time discretization. The simulations focus on the effects of several physical parameters, namely Hartmann and Rayleigh numbers, Joule heating parameter, the inclination angle of magnetic field and number of undulation of wavy wall on the flow and temperature distribution. Moreover, the stability analysis of the numerical method is performed in terms of time increment and time relaxation parameters for various combinations of the problem controlling parameters.

Wind Shielding Impacts on Water Quality in an Urban Reservoir

This study applied an atmospheric Computational Fluid Dynamics (CFD) model and a three-dimensional hydrodynamic-ecological lake model to investigate the impacts of variable wind forcing on lake hydrodynamics and water quality. The CFD model was used to predict the wind field over the lake surface which served as the meteorological forcing for the lake model. The study was carried out for the Marina Reservoir in downtown Singapore where field measurements of the wind field showed that temporal and spatial differences in wind field were found to be significant. By comparing simulations using uniform and spatially variable wind inputs in terms of thermal stratification, Richardson number, vorticity, and spatial gradients, this study demonstrates that the variability in wind forcing in urban lakes that arise from shielding and seasonal effects can have significant impacts on the hydrodynamics and water quality in the reservoir.

A remark on the existence of a class of stretched [formula omitted] Magnetohydrodynamics flow

We consider the existence of a class of stretched solutions of 212D Magnetohydrodynamics equations in R3, which are sometimes called the columnar or two and half dimensional flows. The third components of the state variables have the form u3=x3γ1(x1,x2)+φ1(x1,x2) and B3=x3γ2(x1,x2)+φ2(x1,x2) and the first two components of the state variables depend on x1 and x2 only. We prove the local existence of such a flow in Sobolev spaces and give the regularity criteria in terms of 2D vorticity ω or 2D magnetic density j (but not both). Next, we identify the global existence of a class of axisymmetric flow without swirl for both velocity and magnetic field as a corollary of the main theorem. Finally, we present some exact global solutions as well as singular solutions with a special structure for viscous case and some exact global solutions for full inviscid case.

Shed vortex structure and phase-averaged velocity statistics in symmetric/asymmetric turbulent flat plate wakes

The near wake of a flat plate is investigated via direct numerical simulations. Many earlier experimental investigations have used thin plates with sharp trailing edges and turbulent boundary layers to create the wake. This results in large θ/DTE values (θ is the boundary layer momentum thickness toward the end of the plate and DTE is the trailing edge thickness). In the present study, the emphasis is on relatively thick plates with circular trailing edges (CTEs) resulting in θ/D values less than one (D is the plate thickness and the diameter of the CTE) and vigorous vortex shedding. The Reynolds numbers based on the plate length and D are 1.255 × 106 and 10 000, respectively. Two cases are computed: one with turbulent boundary layers on both the upper and lower surfaces of the plate (statistically the same, symmetric wake, Case TT) and the other with turbulent and laminar boundary layers on the upper and lower surfaces, respectively (asymmetric case, Case TL). The data and understanding obtained are of considerable engineering interest, particularly in turbomachinery where the pressure side of an airfoil can remain laminar or transitional because of a favorable pressure gradient and the suction side is turbulent. Shed-vortex structure and phase-averaged velocity statistics obtained in the two cases are compared here. The upper negative shed vortices in Case TL (turbulent separating boundary layer) are weaker than the lower positive ones (laminar separating boundary layer) at inception (a factor of 1.27 weaker in terms of peak phase-averaged spanwise vorticity at the first appearance of a peak). The upper vortices weaken rapidly as they travel downstream. A second feature of interest in Case TL is a considerable increase in the peak phase-averaged, streamwise normal intensity (random component) with increasing streamwise distance (x/D) that occurs near the positive vortex cores. This behavior is observed for a few diameters in the near wake. This is counter to Case TT where the peak value essentially decreases with increasing x/D. Both these effects are examined in detail, and the important contributors are identified.

Experimental investigation of the flow around a simplified ground vehicle under effects of the steady crosswind

Crosswinds which stem from on-road flow conditions can deteriorate a ground vehicle's driving performance. In spite of the numerous studies investigating aerodynamics of the ground vehicles in the previous literature, there is still a need for thorough understanding of the underlying flow phenomena related to crosswind sensitivity of the ground vehicles. Therefore, the present study is aimed to investigate characteristics of the flow features around the ground vehicles under steady crosswind conditions within a range of yaw angles 0° ≤ β ≤ 15° using the Ahmed vehicle model with rear slant angles of α = 25° and 35°. Throughout the investigations, flow visualizations using dye injection technique and velocity measurements using particle image velocimetry PIV technique are conducted. The Reynolds number of the flow which is based on the free stream flow velocity U = 200 mm/s and height of the model H = 72 mm is ReH = 1.4 × 104. Results are presented in terms of time-averaged vorticity <ω> contours and streamline <ψ> patterns together with velocity magnitude ((<u>2+<w>2)1/2/U) of the flow fields. Additionally, turbulence quantities such as Reynolds stresses <u'w'>/U2 and turbulent kinetic energy TKE are presented and discussed in details. Results of the present study show that characteristics of the flow features in the near wake region downstream of the Ahmed model are very sensitive to the effects of the crosswind.

Combined effects of the velocity and the aspect ratios on the bifurcation phenomena in a two-sided lid-driven cavity flow

PurposeThis paper aims to analyze the effect of aspect ratio A and aspect velocity ratio a on the bifurcation occurrence phenomena in lid-driven cavity by using finite volume method (FVM) and multigrid acceleration. This study has been performed for certain pertinent parameters; a wide range of the Reynolds number values has been adopted, and aspect ratios ranging from 0.25 to 1 and various velocity ratios from 0.25 to 0.825 have been considered in this investigation. Results show that the transition to the unsteady regime follows the classical scheme of Hopf bifurcation, giving rise to a perfectly periodic state. Flow periodicity has been verified through time history plots for the velocity component and phase-space trajectories as a function of Reynolds number. Velocity profile for special case of a square cavity (A = 1) was found to be in good agreement between current numerical results and published ones. Flow characteristics inside the cavity have been presented and discussed in terms of streamlines and vorticity contours at a fixed Reynolds number (Re = 5,000) for various aspect ratios (a = 0).Design/methodology/approachThe numerical method is based on the FVM and multigrid acceleration.FindingsComputations have been investigated for several Reynolds numbers and aspect ratios A (0.25, 0.5, 0.75, 0.825 and 1). Besides, various velocity ratios (a = 0.25, 0.5, 0.75 and 0.825) at fixed aspect ratios (A = 0.25, 0.5 and 0.75) were considered. It is observed that the transition to the unsteady regime follows the classical scheme of Hopf bifurcation, giving rise to a perfectly periodic state. Flow periodicity is verified through time history plots for velocity components and phase-space trajectories.Originality/valueThe bifurcations between steady and unsteady states are investigated.

Orthogonal Collocation on Finite Element Method for Lid-Driven Cavity Flow

Electrical Energy Storage (EES), especially the Redox Flow Batteries (RFB) are expected to play a critical role in the integration of renewable energy with microgrids. However, despite its flexibility in capacity and long-term stability, the performance of EES greatly depends on fluid dynamics in the RFB, in particular for the study of long-term durability and degradation analysis. To maximize the performance and enable model-based design, analysis, and control, efficient simulation of RFB behavior is essential. In this study, Orthogonal Collocation on Finite Element (OCFE) approach is introduced and validated for the classical lid-driven cavity flow problem. The Navier-Stokes (N-S) equation is mathematically reformulated in terms of stream function and vorticity. The cavity is spatially discretized into subdomains, while the state variables are defined at the collocation points in each subdomain. The numerical result shows good agreement with published literature while reducing the computational time.

Aerothermal Characteristics of Solid and Slitted Pentagonal Rib Turbulators

This work is an experimental study of detailed aerothermal characteristics inside a duct carrying an array of solid and permeable pentagonal ribs with a parallel and inclined slit, mounted on the bottom wall. The rib height-to-hydraulic diameter ratio, the rib pitch-to-height ratio, and the open area ratio fixed during experiments are 0.125%, 12%, and 25%, respectively. The heat transfer coefficient (HTC) distribution is mapped by using transient liquid crystal thermography (LCT), while the detailed flow measurements are performed by using particle image velocimetry (PIV). The primary focus of the study is to assess the influence of inter-rib region flow characteristics on the local heat transfer fields. The heat transfer and friction factor measurements are evaluated along with thermohydraulic performances at different Reynolds numbers, i.e., 26,160, 42,500, and 58,850. Performance indexes show that the pentagonal ribs with the inclined-slit are superior to other configurations from both perspective. Aerothermal features within inter-rib region were elucidated by analyzing the time-averaged streamlines, mean velocities, fluctuation statistics, vorticity, turbulent kinetic energy (TKE) budget terms, and local and spanwise-averaged Nusselt number as well as augmentation Nusselt numbers. Critical flow structures and coherent structures were identified, which illustrate about different flow dynamic processes. The flow emanating out of the inclined-slit pentagonal rib significantly affects the magnitude of streamwise velocity, fluctuation statistics, vorticity, and TKE budget terms at the downstream corner, whereas the dissipation term of TKE budget correlates well with the surface heat transfer distribution.

On Approaches to Solving the Problem of an Interface Deformation in a Two-Layer System with Evaporation

Mathematical modeling of the two-layer convective fluid flows is performed by the Oberbeck — Boussinesq equations and relations at the thermocapillary interface. Special attention should be paid to the problems with mass transfer at the interfaces. In particular, mass transfer can be a result of evaporation or condensation. Also, the problems with the vapor diffusion and thermodiffusion and diffusive thermal conductivity effects in the gas-liquid layers should be considered. The new solutions of the convection equations are presented to model two-layer flows. The flows are induced by the action of a longitudinal temperature gradient in the transversely directed gravity field. The interface assumed to be rectilinear when developing the analytical solution. The problem of finding the real interface position is solved with the help of the interface conditions. A derivation of the kinematic and dynamic conditions in terms of stream function and vorticity and an equation for the tangential velocity at interface is presented. A method of determination of a smooth deformable interface is discussed.DOI 10.14258/izvasu(2018)1-12

On a vorticity-based formulation for reaction-diffusion-Brinkman systems

We are interested in modelling the interaction of bacteria and certain nutrient concentration within a porous medium admitting viscous flow. The governing equations in primal-mixed form consist of an advection-reaction-diffusion system representing the bacteria-chemical mass exchange, coupled to the Brinkman problem written in terms of fluid vorticity, velocity and pressure, and describing the flow patterns driven by an external source depending on the local distribution of the chemical species. A priori stability bounds are derived for the uncoupled problems, and the solvability of the full system is analysed using a fixed-point approach. We introduce a primal-mixed finite element method to numerically solve the model equations, employing a primal scheme with piecewise linear approximation of the reaction-diffusion unknowns, while the discrete flow problem uses a mixed approach based on Raviart-Thomas elements for velocity, Nedelec elements for vorticity, and piecewise constant pressure approximations. In particular, this choice produces exactly divergence-free velocity approximations. We establish existence of discrete solutions and show their convergence to the weak solution of the continuous coupled problem. Finally, we report several numerical experiments illustrating the behaviour of the proposed scheme.

Численный анализ турбулентных режимов сопряженного конвективно-радиационного теплопереноса в замкнутой области со стеклянной стенкой

Mathematical simulation of unsteady turbulent natural convection and thermal surface radiation in a closed cavity with solid heat-conducting walls of finite thickness in the presence of a heat source of constant temperature has been carried out. The governing equations for the conservation of mass, momentum, and energy have been written using a system of partial differential equations in terms of stream function, temperature and vorticity. The boundary-value problem has been solved by the finite difference method. The effect of turbulence has been modeled using the standard model. The effects of the surface emissivity and the nonstationary factor on the fluid flow and heat transfer have been studied. As a result of the studies, distributions of both local (isolines of the stream function and temperature) and integral (average radiative and convective Nusselt numbers) characteristics have been obtained. It has been shown that an increase in the surface emissivity leads to a modification of flow patterns and the heat transfer enhancement.

Quark-hadron duality in hydrodynamics: an example

We consider the problem of transferring overall rotation of quark-gluon plasma to polarization of hyperons along the rotation axis. As a toy theoretical model, we exploit that of pionic superfluidity induced by chemical potentials violating isotopic symmetry. Apparently, the model accounts only for the light degrees of freedom, that is pions. The rotation, however, results in vortices which are infinitely thin in the hydrodynamic approximation. Field theory resolves the singularity and predicts that the core of the vortices is build up on spins of baryons. We review consequences from the quark-hadron duality in this case. First, an anomalous triangle graph in effective field theory turns to be dual to the vorticity term in the standard hydrodynamic expansion. And, then, the overall coefficient determining the polarization of baryons is fixed by duality with the triangle graph in the fundamental field theory.

Influence of air change rates on indoor CO2 stratification in terms of Richardson number and vorticity

Above rules-of-thumb ventilation standard based on air change rate per hour (ACH), it is necessary to assess the indoor airflow and indoor air quality (IAQ) with respect to simple dimensionless numbers from the practical point of view. Hence, this work aims at investigating the influence of air change rates on indoor CO2 stratification and removal with dimensionless time scale ratio (proportional to Ri/α, Richardson number Ri, mass flux ratio α) and vorticity by applying experiment and simulation methods. We firstly carried out a series of experiments with different ACHs along with constant CO2 pollutant sources, further for simulation validation. Next, numerical simulation was employed to investigate five different ACHs (ranged from 4 to 28) on indoor CO2 concentration for two different vent-inlet-size cases. It was found that as the increase of ACH, the averaging outlet CO2 concentration was decreased until ACH equal to 16, both cases starting showing asymptotic behavior. When looking at indoor CO2 distribution, the case with larger vent-inlet size showed clear stratification even with higher ACH value (i.e., 28), due to the relatively smaller vorticity value (i.e., 0.47, with 3.14 for small-vent-size case) and larger Ri magnitude (37 times) compared to the small-vent-size case. Specifically, it is beneficial for indoor CO2 removal to keep time scale ratio Ri/α below 10−3 and vorticity above 1 rather than merely following with high ACH values. These findings will be of great importance for practical applications to design and control ventilation systems in the perspective of health and energy efficiency.

Experimental investigation of flow over a square cylinder with an attached splitter plate at intermediate reynolds number

The present work is an experimental investigation of flow control over a square cylinder using an attached splitter plate. The experiments are mainly conducted at a Reynolds number of 485. A splitter plate of varying length from 0 to 6 times of the cylinder width is attached to the rear side of the square cylinder to control the flow. The thickness of the splitter plate is kept constant at 10% of cylinder width. The flow interference of a square cylinder with an attached splitter plate is observed using PIV, Hot wire and flow visualization techniques. The primary focus is given on the flow structure and related forces. From the experiments, it has been observed that a secondary vortex appears at the tail edge of the plate after a particular length of the splitter plate. This vortex rotation is opposite to the main vortex and it influences the primary vortex shedding as well as shear layer formation. As a result, the plate modifies the wake size and flow structure behind the cylinder. The drag coefficient and the Strouhal number decrease with an increase in splitter plate length. A correlation is found between the splitter plate length, Reynolds number, and the drag coefficient. The effect of the splitter plate length on the flow field is also studied in terms of velocity, vorticity, streamlines, recirculation length, and turbulence statistics.

Particle temperature and the chiral vortical effect in the early universe

We study the effect of hotter or colder particles on the evolution of the chiral magnetic field in the early universe. We are interested in the temperature-dependent term in the chiral vortical effect (CVE). There are no changes in the magnetic energy spectrum at large length scales but in the Kolmogorov regime we do find a difference. Our numerical results show that the Gaussian peak in the magnetic spectrum becomes negatively skewed. The negatively skewed peak can be fitted with a beta distribution. Analytically, one can relate the non-Gaussianity of the distribution to the temperature-dependent vorticity term. The vorticity term is therefore responsible for the beta distribution in the magnetic spectrum. Since the beta distribution has already been used to model turbulent dispersion in fluids, hence it seems that the presence of hotter or colder particles may lead to turbulence in the magnetized plasma.

Climatology of the meteorological factors associated with haze events over northern China and their potential response to the Quasi-Biannual Oscillation

An upswing in haze weather during autumn and winter has been observed over North and Northeast China in recent years, imposing adverse impacts upon local socioeconomic development and human health. However, such an increase in the occurrence of haze events and its association with natural climate variability and climate change are not well understood. To investigate the climatology of the meteorological factors associated with haze events and their natural variability, this study uses a meteorological pollution index called PLAM (Parameter Linking Air-quality to Meteorological conditions) and ERA-Interim reanalysis data. The results suggest that high PLAM values tend to occur over southern parts of northern China, implying the weather conditions over this area are favorable for the occurrence of haze weather. For the period 1979–2014, the regional mean PLAM shows an overall increase across Beijing, Tianjin, and Hebei Province, and parts of Shanxi Province. Also, a periodicity of 28–34 months is found in the temporal variation of PLAM, which implies a potential association of PLAM with the stratospheric Quasi-Biannual Oscillation (QBO). By using the QBO index during the autumn and winter seasons in the preceding year, an increase in PLAM is found for the westerly phases of the QBO, relative to the easterly phases. An upper-tropospheric warming is also found in the westerly phases, which can induce a stable stratification that favors the increase in PLAM across the midlatitudes. The modulations of large-scale environmental factors, including moist static stability, vertical velocity, and temperature advection, also act to enhance PLAM in the westerly phases. However, the baroclinic term of moist potential vorticity at 700 hPa tends to decrease over the south, and an increase in low-level ascent is found over the north. These factors can reduce PLAM and possibly limit the statistical significance of the increased PLAM in the westerly phases of the QBO.

Numerical investigation of the effects of camber ratio on the hydrodynamic performance of a marine propeller

In this research, effects of the camber ratio distribution over the blades of a NACA marine propeller were numerically investigated on its open water hydrodynamic performance characteristic curves. To investigate this problem, Reynolds averaged Navier-Stokes (RANS) equations were solved using computational fluid dynamics (CFD). Results are presented in terms of vorticity, pressure coefficient, hydrodynamic efficiency, thrust and torque coefficients, and hydrodynamic performance characteristic curves. Results show that the location of the maximum efficiency of the propeller is unchanged versus advance coefficient by changing the camber ratio over the blades. It is shown that magnitudes of the efficiency, torque, thrust, vorticity, pressure coefficient, and the width of the efficiency curve are changed non-linearly by changing the camber ratio.

Drag Reduction on a Square Cylinder using Multiple Detached Control Cylinders

A two-dimensional numerical simulation for flow over a main cylinder with detached controlling cylinders placed at different position is performed through Lattice Boltzmann Method (LBM) to reduce fluid forces. For this study the Reynolds number (Re) is fixed at 160, while gap ratio between these cylinders are taken in the range from 0.5 to 8. The results yield in terms of vorticity, time-series analysis of drag and lift coefficients, power spectra of lift coefficients and force statistics. Depending on gap spacing, flow is classified into four different patterns, called as (i) single blender body, (ii) shear layer reattachment, (iii) fully developed flow and (iv) vortex suppression fully developed flow patterns. In comparison of all three configurations, it is examined that the maximum value of Cdmean and Strouhal number occurs for downstream configuration. Whereas, upstream and dual configuration play a vital role to reduce forces and to suppress vortex shedding. The maximum reduction found in mean drag coefficient for downstream, upstream and for dual configuration is 8.3%, 51% and 50.8%, respectively. Whereas, the reduction in Clrms values for all three configurations is 84.4%, 58.2% and 86.4%, respectively.