Showing papers on "Velocity gradient published in 2019"

Explicit formula for the Liutex vector and physical meaning of vorticity based on the Liutex-Shear decomposition

Abstract: In the present study, the physical meaning of vorticity is revisited based on the Liutex-Shear (RS) decomposition proposed by Liu et al. in the framework of Liutex (previously called Rortex), a vortex vector field with information of both rotation axis and swirling strength (Liu et al. 2018). It is demonstrated that the vorticity in the direction of rotational axis is twice the spatial mean angular velocity in the small neighborhood around the considered point while the imaginary part of the complex eigenvalue (λci) of the velocity gradient tensor (if exist) is the pseudo-time average angular velocity of a trajectory moving circularly or spirally around the axis. In addition, an explicit expression of the Liutex vector in terms of the eigenvalues and eigenvectors of velocity gradient is obtained for the first time from above understanding, which can further, though mildly, accelerate the calculation and give more physical comprehension of the Liutex vector.

Comparative analysis between 36 nm and 47 nm alumina–water nanofluid flows in the presence of Hall effect

Abstract: White crystalline powder (aluminum oxide $$-\hbox {Al}_2\hbox {O}_3$$ ) and water are the products often formed after the heating of aluminum hydroxide. In this report, boundary layer flow of two different nanofluids (i.e., 36 nm $$\hbox {Al}_2\hbox {O}_3$$ -water and 47 nm $$\hbox {Al}_2\hbox {O}_3$$ -water) over an upper horizontal surface of a paraboloid of revolution under the influence of magnetic field is presented. The combined influence of magnetic field strength, electric current density, electric charge, electron collision time, and the mass of an electron in the flows are considered in the governing equations. Three-dimensional transport phenomenon was considered due to the influence of the Lorentz force $$(\vec {F})$$ along the z-direction as in the case of Hall currents. In this study, the dynamic viscosity and density of the nanofluids are assumed to vary with the volume fraction $$\phi$$ . The dimensional governing equations were non-dimensionalization and parametrization using similarity variables. The corresponding boundary value problem was transformed into initial value problem using the method of superposition and solved numerically using fourth-order Runge–Kutta method with shooting technique (RK4SM). Magnetic field parameter is seen to have dual effects on the cross-flow velocity profiles of both nanofluids. The maximum cross-flow velocity is attained within the fluid domain when 36 nm nanoparticles alumina is used. The cross-flow velocity gradient at the wall increases with magnetic field parameter (M) and also increases significantly with Hall parameter at larger values of M.

Magnetic field morphology in interstellar clouds with the velocity gradient technique

Abstract: Magnetic fields, while ubiquitous in many astrophysical environments, are challenging to measure observationally. Based on the properties of anisotropy of eddies in magnetized turbulence, the velocity gradient technique is a method synergistic to dust polarimetry that is capable of tracing plane-of-the-sky magnetic fields, measuring the magnetization of interstellar media and estimating the fraction of gravitational collapsing gas in molecular clouds using spectral line observations. Here, we apply this technique to five low-mass star-forming molecular clouds in the Gould Belt and compare the results to the magnetic field orientation obtained from polarized dust emission. We find that the estimates of magnetic field orientations and magnetization for both methods are statistically similar. We estimate the fraction of collapsing gas in the selected clouds. By using the velocity gradient technique, we also present the plane-of-the-sky magnetic field orientation and magnetization of the Smith Cloud, for which dust polarimetry data are unavailable. The velocity gradient technique is used to measure the magnetic field orientations and magnetization of five low-mass star-forming molecular clouds, also finding that collapsing regions constitute a small fraction of the volume in these clouds.

An objective version of the Rortex vector for vortex identification

Abstract: Vortices are a ubiquitous natural phenomenon, and their structure, shape, and characteristics should be independent of the observer, which implies that the vortex identification method or vortex definition should maintain its objectivity. Currently, most of the vortex identification methods rely on velocity gradient tensors. The calculation of the velocity gradient tensor is based on the reference frame of the observer, and the velocity gradient tensor will vary with the observer’s motion. By these vortex identification methods, very different vortex structures could be visualized and described in a moving reference frame. Recently, a mathematical definition of the Rortex vortex vector was proposed to represent the local fluid rotation. The definition used velocity gradient tensor to derive the local rigid rotation axis and strength. However, the original definition of the Rortex vector is nonobjective. In order to obtain the objectivity, in this paper, by a definition of a net velocity gradient tensor, an objective Rortex vortex vector is defined which uses a spatially averaged vorticity to offset the impact of the motion frame. Some typical numerical examples, such as an implicit large-eddy simulation result for shock and boundary layer interaction and a direct numerical simulation for boundary layer transition, are provided to show the objectivity of the developed method.

Numerical investigation of heat transfer of laminar and turbulent pulsating Al2O3/water nanofluid flow

Abstract: The purpose of this paper is to investigate the heat transfer of laminar and turbulent pulsating Al203/water nanofluid flow in a two-dimensional channel. In the laminar flow range, with increasing Reynolds number (Re), the velocity gradient is increased. Also, the Nusselt number (Nu) is increased, which causes increase in the overall heat transfer rate. Additionally, in the change of flow regime from laminar to turbulent, average thermal flux and pulsation range are increased. Also, the effect of different percentage of Al2O3/water nanofluid is investigated. The results show that the addition of nanofluids improve thermal performance in channel, but the using of nanofluid causes a pressure drop in the channel.,The pulsatile flow and heat transfer in a two-dimensional channel were investigated.,The numerical results show that the Al2O3/Water nanofluid has a significant effect on the thermal properties of the different flows (laminar and turbulent) and the average thermal flux and pulsation ranges are increased in the change of flow regime from laminar to turbulent. Also, the addition of nanofluid improves thermal performance in channels.,The originality of this work lies in proposing a numerical analysis of heat transfer of pulsating Al2O3/Water nanofluid flow -with different percentages- in the two-dimensional channel while the flow regime change from laminar to turbulent.

ALMA resolves the hourglass magnetic field in G31.41+0.31

Abstract: Context. Submillimeter Array (SMA) 870 μ m polarization observations of the hot molecular core G31.41+0.31 revealed one of the clearest examples up to date of an hourglass-shaped magnetic field morphology in a high-mass star-forming region.Aims. To better establish the role that the magnetic field plays in the collapse of G31.41+0.31, we carried out Atacama Large Millimeter/ submillimeter Array (ALMA) observations of the polarized dust continuum emission at 1.3 mm with an angular resolution four times higher than that of the previous (sub)millimeter observations to achieve an unprecedented image of the magnetic field morphology.Methods. We used ALMA to perform full polarization observations at 233 GHz (Band 6). The resulting synthesized beam is 0′′.28×0′′.20 which, at the distance of the source, corresponds to a spatial resolution of ~875 au.Results. The observations resolve the structure of the magnetic field in G31.41+0.31 and allow us to study the field in detail. The polarized emission in the Main core of G31.41+0.41is successfully fit with a semi-analytical magnetostatic model of a toroid supported by magnetic fields. The best fit model suggests that the magnetic field is well represented by a poloidal field with a possible contribution of a toroidal component of ~10% of the poloidal component, oriented southeast to northwest at approximately −44° and with an inclination of approximately −45°. The magnetic field is oriented perpendicular to the northeast to southwest velocity gradient detected in this core on scales from 103 to 104 au. This supports the hypothesis that the velocity gradient is due to rotation of the core and suggests that such a rotation has little effect on the magnetic field. The strength of the magnetic field estimated in the central region of the core with the Davis–Chandrasekhar-Fermi method is ~8–13 mG and implies that the mass-to-flux ratio in this region is slightly supercritical.Conclusions. The magnetic field in G31.41+0.31 maintains an hourglass-shaped morphology down to scales of <1000 au. Despite the magnetic field being important in G31.41+0.31, it is not enough to prevent fragmentation and collapse of the core, as demonstrated by the presence of at least four sources embedded in the center of the core.

Drag-reduction of 3D printed shark-skin-like surfaces

Abstract: The marvels of the slippery and clean sharkskin have inspired the development of many clinical and engineering products, although the mechanisms of interfacial interaction between the sharkskin and water have yet to be fully understood. In the present research, a methodology was developed to evaluate morphological parameters and to enable studying the effects of scale orientation on the fluidic behavior of water. The scale orientation of a shark skin was defined as the angle between the ridges and fluid flow direction. Textured surfaces with a series orientation of scales were designed and fabricated using 3D printing of acrylonitrile butadiene styrene (ABS). The fluid drag performance was evaluated using a rheometer. Results showed that the shark–skin-like surface with 90 degree orientation of scales exhibited the lowest viscosity drag. Its maximum viscosity reduction was 9%. A viscosity map was constructed based on the principals of fluid dynamic. It revealed that the drag reduction effect of a shark-skin-like surface was attributed to the low velocity gradient. This was further proven using diamond nitrogen-vacancy sensing where florescent diamond particles were distributed evenly when the velocity gradient was at the lowest. This understanding could be used as guidance for future surface design.

Tracing Multi-scale Magnetic Field Structure Using Multiple Chemical Tracers in Giant Molecular Clouds

Abstract: Probing magnetic fields in Giant Molecular Clouds is often challenging. Fortunately, recently simulations show that analysis of velocity gradients (the Velocity Gradient Technique) can be used to map out the magnetic field morphology of different physical layers within molecular clouds when applied CO isotopologues with different optical depths. Here, we test the effectiveness of the Velocity Gradient Technique in reconstructing the magnetic field structure of the molecular cloud Vela C, employing seven chemical tracers that have different optical depths, i.e. 12CO, 13CO, C18O, CS, HNC, HCO+, and HCN. Our results show good correspondence between the magnetic field morphology inferred from velocity gradients using these different molecular tracers and the magnetic field morphology inferred from BLASTPol polarization observations. We also explore the possibility of using a combination of velocity gradients for multiple chemical tracers to explain the structure of the magnetic field in molecular clouds. We search for signatures of gravitational collapse in the alignment of the velocity gradients and magnetic field and conclude that collapsing regions constitute a small fraction of the cloud.

Tracing Magnetic Field Morphology Using the Velocity Gradient Technique in the Presence of CO Self-absorption

Abstract: Probing magnetic fields in self-gravitating molecular clouds are generally difficult even with the use of the polarimetry. Based on the properties of magneto-hydrodynamic (MHD) turbulence and turbulent reconnection, Velocity Gradient Technique (VGT) provides a new way in tracing magnetic field orientation and strength based on the spectroscopic data. Our study tests the applicability of VGT in various molecular tracers, e.g. 12CO, 13CO, and C18O. By inspecting synthetic molecular line maps of CO isotopologue generated through radiative transfer calculations, we show that the VGT method can be successfully applied in probing the magnetic field direction in the diffuse interstellar medium as well as in self-gravitating molecular clouds.

Entropy generation of turbulent Cu–water nanofluid flow in a heat exchanger tube fitted with perforated conical rings

Abstract: Entropy generation analysis for the Cu–water nanofluid flow through a heat exchanger tube equipped with perforated conical rings is numerically investigated. Frictional and thermal entropy generation rates are defined as functions of velocity and temperature gradients. Governing equations are solved by using finite volume method, and Reynolds number is in the range of 5000–15,000. The effects of geometrical and physical parameters such as Reynolds number, number of holes and nanoparticles volume fraction on the thermal and viscous entropy generation rates and Bejan number are investigated. The results indicate that the thermal irreversibility is dominant in most part of the tube. But it decreases with increasing the nanoparticle volume fraction. Frictional entropy generation reduces with increasing the number of holes from 4 to 10. This is because of stronger velocity gradient near the perforated holes. Bejan number decreases with augment of Reynolds number.

A smoothed particle hydrodynamics simulation of fiber-filled composites in a non-isothermal three-dimensional printing process

Abstract: The mechanical and thermal behavior of nonisothermal fiber-filled composites in a three-dimensional printing process is studied numerically with a smoothed particle hydrodynamics method. A classical microstructure-based fiber suspension model with a temperature-dependent power-law viscosity model and a microstructure constitutive model is implemented to model a fiber-filled system. The fiber microstructure is described by a second-order tensor A2 which describes the spatially averaged orientation of the fibers. Two benchmark cases are presented to validate the reliability of the present implementation. Three typical printing modes are tested to assess the characteristics of printed layers. The results show that the printed layer becomes thicker, and the fiber alignment in the printing direction is enhanced in the bottom half of the layer and reduced in the top half due to the existence of nonisothermal effects in the process. The variation in fiber orientation becomes larger with increasing fiber concentration. By increasing the Peclet number, the deposited layer thickness reduces and the fiber alignment in the printing direction is enhanced in the top half and reduced in the bottom half. The evolution of the orientation and the velocity gradient tensors projected along several streamlines are discussed to illustrate the effects of the temperature and different printing modes on the deposited layer.

Gas velocity structure of the Orion A integral-shaped filament

Abstract: We present analysis of the gas kinematics of the Integral Shaped Filament (ISF) in Orion~A using four different molecular lines, $^{12}$CO (1-0), $^{13}$CO (1-0), NH$_3$ (1,1), and N$_2$H$^+$ (1-0). We describe our method to visualize the position-velocity (PV) structure using the intensity-weighted line velocity centroid, which enables us to identify structures that were previously muddled or invisible. We observe a north to south velocity gradient in all tracers that terminates in a velocity peak near the center of the Orion Nebula Cluster (ONC), consistent with the previously reported "wave-like" properties of the ISF. We extract the velocity dispersion profiles and compare the non-thermal line widths to the gas gravitational potential. We find supersonic Mach number profiles, yet the line widths are consistent with the gas being deeply gravitationally bound. We report the presence of two $^{12}$CO velocity components along the northern half of the ISF; if interpreted as circular rotation, the angular velocity is $\omega=1.4\,{\rm Myr}^{-1}$. On small scales we report the detection of N$_2$H$^+$ and NH$_3$ "twisting and turning" structures, with short associated timescales that give the impression of a torsional wave. Neither the nature of these structures nor their relation to the larger scale wave is presently understood.

On the Reynolds number dependence of velocity-gradient structure and dynamics

Abstract: We seek to examine the changes in velocity-gradient structure (local streamline topology) and related dynamics as a function of Reynolds number ( ). The analysis factorizes the velocity gradient ( ) into the magnitude ( ) and normalized-gradient tensor ( ). The focus is on bounded as (i) it describes small-scale structure and local streamline topology, and (ii) its dynamics is shown to determine magnitude evolution. Using direct numerical simulation (DNS) data, the moments and probability distributions of and its scalar invariants are shown to attain independence. The critical values beyond which each feature attains independence are established. We proceed to characterize the dependence of -conditioned statistics of key non-local pressure and viscous processes. Overall, the analysis provides further insight into velocity-gradient dynamics and offers an alternative framework for investigating intermittency, multifractal behaviour and for developing closure models.

Scale interactions in turbulent rotating planar Couette flow: insight through the Reynolds stress transport

Abstract: In turbulent planar Couette flow under anticyclonic spanwise system rotation, large-scale roll-cell structures arise due to a Coriolis-force-induced instability. The structures are superimposed on smaller-scale turbulence, and with increasing angular velocity (. It is also shown that at such an intermediate rotation number the roll cells interact with smaller scales by moving near-wall structures towards the core region of the channel, by which the Reynolds stress is transported from relatively small scales near the wall towards larger scales in the channel centre. Such Reynolds stress transport by scale interaction becomes increasingly significant as the Reynolds number increases, and results in a reversed mean velocity gradient at the channel centre at high enough Reynolds numbers.

Numerical scheme for simulation of transient flows of non-Newtonian fluids characterised by a non-monotone relation between the symmetric part of the velocity gradient and the Cauchy stress tensor

Abstract: We propose a numerical scheme for simulation of transient flows of incompressible non-Newtonian fluids characterised by a non-monotone relation between the symmetric part of the velocity gradient (shear rate) and the Cauchy stress tensor (shear stress). The main difficulty in dealing with the governing equations for flows of such fluids is that the non-monotone constitutive relation allows several values of the stress to be associated with the same value of the symmetric part of the velocity gradient. This issue is handled via a reformulation of the governing equations. The equations are reformulated as a system for the triple pressure–velocity–apparent viscosity, where the apparent viscosity is given by a scalar implicit equation. We prove that the proposed numerical scheme has—on the discrete level—a solution, and using the proposed scheme, we numerically solve several flow problems.

A higher-order Lagrangian discontinuous Galerkin hydrodynamic method for elastic–plastic flows

Abstract: We present a new high-order Lagrangian discontinuous Galerkin (DG) hydrodynamic method for gas and solid dynamics. The evolution equations for specific volume, momentum, and total energy are discretized using the modal DG approach. The specific volume, velocity, and specific total energy fields are approximated with up to quadratic Taylor series polynomials. The specific internal energy, pressure, and stress deviators are nodal quantities. The stress deviators are evolved forward in time using a hypoelastic–plastic approach, which requires a velocity gradient. A new method is presented for calculating a high-order polynomial for the velocity gradient in an element. Plasticity is handled by applying a radial return model to the stress deviators. Limiting approaches are presented for modal and nodal fields. The TVD RK time integration method is used to temporally advance all governing evolution equations. Generalized Lagrangian DG equations are derived but test problems are calculated for 1D Cartesian coordinates. A suite of gas and solid dynamics test problem results are calculated to demonstrate the stability and formal accuracy of the new Lagrangian DG method.

Gravity, Magnetic Field, and Turbulence: Relative Importance and Impact on Fragmentation in the Infrared Dark Cloud G34.43+00.24

Abstract: (Abbreviated) We investigate the interplay between magnetic (B) field, gravity, and turbulence in the fragmentation process of cores within the filamentary infrared dark cloud G34.43+00.24. We observe the magnetic field (B) morphology across G34.43 and compare with the kinematics obtained from N2H+ across the filament. We derive local velocity gradients from N2H+, tracing motion in the plane of sky, and compare with the observed local B field orientations in the plane of sky. Besides a large-scale east-west velocity gradient, we find a close alignment between local B field orientations and local velocity gradients toward the MM1/MM2 ridge. This local correlation in alignment suggests that gas motions are influenced by the magnetic field morphology or vice versa. Additionally, this alignment seems to be getting even closer with increasing integrated emission in N2H+, possibly indicating that a growing gravitational pull is more and more aligning B field and gas motion. We analyze and quantify B field, gravity, turbulence, and their relative importance toward the MM1, MM2 and MM3 regions with various techniques over two scales, a larger clump area at 2 pc scale and the smaller core area at 0.6 pc scale. While gravitational energy, B field, and turbulent pressure all grow systematically from large to small scale, the ratios among the three constituents develop clearly differently over scale. We propose that this varying relative importance between B field, gravity, and turbulence over scale drives and explains the different fragmentation types seen at sub-pc scale (no fragmentation in MM1; aligned fragmentation in MM2; clustered fragmentation in MM3). We discuss uncertainties, subtleties, and the robustness of our conclusion, and we stress the need of a multi-scale joint analysis to understand the dynamics in these systems.

Droplets. II. Internal Velocity Structures and Potential Rotational Motions in Pressure-dominated Coherent Structures

Abstract: We present an analysis of the internal velocity structures of the newly identified sub-0.1 pc coherent structures, droplets, in L1688 and B18. By fitting 2D linear velocity fields to the observed maps of velocity centroids, we determine the magnitudes of linear velocity gradients and examine the potential rotational motions that could lead to the observed velocity gradients. The results show that the droplets follow the same power-law relation between the velocity gradient and size found for larger-scale dense cores. Assuming that rotational motion giving rise to the observed velocity gradient in each core is a solid-body rotation of a rotating body with a uniform density, we derive the "net rotational motions" of the droplets. We find a ratio between rotational and gravitational energies, $\beta$, of $\sim 0.046$ for the droplets, and when including both droplets and larger-scale dense cores, we find $\beta \sim 0.039$. We then examine the alignment between the velocity gradient and the major axis of each droplet, using methods adapted from the histogram of relative orientations (HRO) introduced by Soler et al. (2013). We find no definitive correlation between the directions of velocity gradients and the elongations of the cores. Lastly, we discuss physical processes other than rotation that may give rise to the observed velocity field.

Connecting the Scales: Large Area High-resolution Ammonia Mapping of NGC 1333

Abstract: We use NH3 inversion transitions to trace the dense gas in the NGC 1333 region of the Perseus molecular cloud. NH3(1,1) and NH3(2,2) maps covering an area of 102 square arcminutes at an angular resolution of ~3.7" are produced by combining VLA interferometric observations with GBT single dish maps. The combined maps have a spectral resolution of 0.14 km/s and a sensitivity of 4 mJy/beam. We produce integrated intensity maps, peak intensity maps and dispersion maps of NH3(1,1) and NH3(2,2) and a line-of-sight velocity map of NH3(1,1). These are used to derive the optical depth for the NH3(1,1) main component, the excitation temperature of NH3(1,1), and the rotational temperature, kinetic temperature and column density of NH3 over the mapped area. We compare these observations with the CARMA J=1-0 observations of N2H+ and H13CO+ and conclude that they all trace the same material in these dense star forming regions. From the NH3(1,1) velocity map, we find that a velocity gradient ridge extends in an arc across the entire southern part of NGC 1333. We propose that a large scale turbulent cell is colliding with the cloud, which could result in the formation of a layer of compressed gas. This region along the velocity gradient ridge is dotted with Class 0/I YSOs, that could have formed from local overdensities in the compressed gas leading to gravitational instabilities. The NH3(1,1) velocity dispersion map also has relatively high values along this region, thereby substantiating the shock layer argument.