Showing papers on "Velocity gradient published in 2020"

A mathematical study of natural convection flow through a channel with non-singular kernels: An application to transport phenomena

Abstract: In this manuscript, we have obtained closed form solution using Laplace transform, inversion algorithm and convolution theorem. The study of mass transfer flow of an incompressible fluid is carried out near vertical channel. Recently, new classes of differential operators have been introduced and recognized to be efficient in capturing processes following the decay law and the crossover behaviors. For the study of heat and mass transfer, we applied the newly differential operators say Atangana-Baleanu ( ABC ) and Caputo-Fabrizio ( CF ) to model such flow. This model for temperature, concentration and velocity gradient is presented in dimensionless form. The obtained solutions have been plotted for various values physical parameters like α , D f , G m , G r , S c and P r on temperature and velocity profile. Our results suggest that for the variation of time the velocity behavior for CF and ABC are reversible. Finally, an incremental value of prandtl number is observed for decrease in the velocity field which reflects the control of thickness of momentum and enlargement of thermal conductivity. Further, dynamical analysis of fluid with memory effect are efficient for ABC as compared to CF.

Velocity Gradient in the Presence of Self-gravity: Identifying Gravity-induced Inflow and Determining Collapsing Stage

Abstract: Understanding how star formation is regulated requires studying the energy balance between turbulence, magnetic fields, stellar feedback, and gravity within molecular clouds. However, identifying the transition region where the gravity takes over remains elusive. Recent studies of the Velocity Gradient Technique (VGT), which is an advanced tool for magnetic field studies, reveal that the gradients of spectroscopic observables change their directions by 90 degrees with respect to the magnetic fields in the regions of gravitational collapse. In this study, we perform 3D MHD numerical simulations. We observe that star formation successfully proceeds in strongly magnetized and fully ionized media. We confirm that the self-gravity induces the change of gradients' orientation and high gradients' amplitude. We explore two ways of identifying collapsing self-gravitating regions through the double-peak feature in the histogram of gradients' orientation and the curvature of gradients. We show that velocity gradients' morphology and amplitude can be synthetically used to trace the convergent inflows. By comparing with the column density Probability Density Functions (N-PDFs) method, we show that VGT is a powerful new tool for studying the gas dynamics and tracing magnetic field in star-forming regions. By analogy with VGT, we extend the Intensity Gradient Technique (IGT) to locate the gravitational collapsing region and shocks. We demonstrate the synergy of VGT and IGT can determine the collapsing stages in a star-forming region.

Hydromagnetic Dissipative and Radiative Graphene Maxwell Nanofluid Flow Past a Stretched Sheet-Numerical and Statistical Analysis

Abstract: The key objective of this analysis is to examine the flow of hydromagnetic dissipative and radiative graphene Maxwell nanofluid over a linearly stretched sheet considering momentum and thermal slip conditions. The appropriate similarity variables are chosen to transform highly nonlinear partial differential equations (PDE) of mathematical model in the form of nonlinear ordinary differential equations (ODE). Further, these transformed equations are numerically solved by making use of Runge-Kutta-Fehlberg algorithm along with the shooting scheme. The significance of pertinent physical parameters on the flow of graphene Maxwell nanofluid velocity and temperature are enumerated via different graphs whereas skin friction coefficients and Nusselt numbers are illustrated in numeric data form and are reported in different tables. In addition, a statistical approach is used for multiple quadratic regression analysis on the numerical figures of wall velocity gradient and local Nusselt number to demonstrate the relationship amongst heat transfer rate and physical parameters. Our results reveal that the magnetic field, unsteadiness, inclination angle of magnetic field and porosity parameters boost the graphene Maxwell nanofluid velocity while Maxwell parameter has a reversal impact on it. Finally, we have compared our numerical results with those of earlier published articles under the restricted conditions to validate our solution. The comparison of results shows an excellent conformity among the results.

Self-gravitating filament formation from shocked flows: velocity gradients across filaments

Abstract: In typical environments of star-forming clouds, converging supersonic turbulence generates shock-compressed regions, and can create strongly-magnetized sheet-like layers. Numerical MHD simulations show that within these post-shock layers, dense filaments and embedded self-gravitating cores form via gathering material along the magnetic field lines. As a result of the preferred-direction mass collection, a velocity gradient perpendicular to the filament major axis is a common feature seen in simulations. We show that this prediction is in good agreement with recent observations from the CARMA Large Area Star Formation Survey (CLASSy), from which we identified several filaments with prominent velocity gradients perpendicular to their major axes. Highlighting a filament from the northwest part of Serpens South, we provide both qualitative and quantitative comparisons between simulation results and observational data. In particular, we show that the dimensionless ratio $C_v \equiv {\Delta v_h}^2/(GM/L)$, where $\Delta v_h$ is half of the observed perpendicular velocity difference across a filament, and $M/L$ is the filament's mass per unit length, can distinguish between filaments formed purely due to turbulent compression and those formed due to gravity-induced accretion. We conclude that the perpendicular velocity gradient observed in the Serpens South northwest filament can be caused by gravity-induced anisotropic accretion of material from a flattened layer. Using synthetic observations of our simulated filaments, we also propose that a density-selection effect may explain observed subfilaments (one filament breaking into two components in velocity space) as reported in Dhabal et al. (2018).

Experimental investigation of internal two-phase flow structures and dynamics of quasi-stable sheet cavitation by fast synchrotron x-ray imaging

Abstract: The quasi-stable sheet cavitation produced in a small Venturi channel is investigated using a fast synchrotron x-ray imaging technique aided with conventional high speed photography. The use of x rays instead of visible light solves cavitation opacity related issues, and x-ray phase contrast-based edge enhancement enables high-definition visualization of the internal two-phase morphology. The simultaneous acquisition of time-resolved velocity and void fraction fields through post-processing of the recorded x-ray images reveals, for the first time, the complex diphasic flow structures inside the sheet cavity, which is essentially divided into six characteristic parts. Distinct from the current mainstream view, the globally steady sheet cavitation is found to be characterized by a weak but constantly existing re-entrant flow that can penetrate the entire cavity. The turbulent velocity fluctuations inside the sheet cavity are also investigated. The turbulence level in the reverse flow region is observed to be as low as in the outer main flow, demonstrating the relatively steady status of the re-entrant flow. Unlike the streamwise and cross-stream fluctuations, the shear stress appears to be weakly correlated with the velocity gradient. The collapse of the vapor phase and the vaporization at the upstream cavity interface are found to be the primary causes of shear stress intensification.

Velocity-coherent filaments in NGC 1333: Evidence for accretion flow?

Abstract: Recent observations of global velocity gradients across and along molecular filaments have been interpreted as signs of gas accreting onto and along these filaments, potentially feeding star-forming cores and proto-clusters. The behavior of velocity gradients in filaments, however, has not been studied in detail, particularly on small scales (< 0.1 pc). In this paper, we present MUFASA, an efficient, robust, and automatic method to fit ammonia lines with multiple velocity components, generalizable to other molecular species. We also present CRISPy, a Python package to identify filament spines in 3D images (e.g., position-position-velocity cubes), along with a complementary technique to sort fitted velocity components into velocity-coherent filaments. In NGC 1333, we find a wealth of velocity gradient structures on a beam-resolved scale of ~0.05 pc. Interestingly, these local velocity gradients are not randomly oriented with respect to filament spines and their perpendicular, i.e., radial, component decreases in magnitude towards the spine for many filaments. Together with remarkably constant velocity gradients on larger scales along many filaments, these results suggest a scenario in which gas falling onto filaments is progressively damped and redirected to flow along these filaments.

Estimation of entropy optimization in Darcy-Forchheimer flow of Carreau-Yasuda fluid (non-Newtonian) with first order velocity slip

Abstract: This research article elaborates the salient attributes of sundry variables i.e., Darcy-Forchheimer number, mixed convection parameter, porosity parameter, Weissenberg number, slip parameter, Prandtl number, activation energy parameter and chemical reaction parameter on the forced convective Darcy-forchheimer flow of non-Newtonian fluid (Carreau-Yasuda fluid) subject to stretchable and flat surface of the sheet. A general mathematical form of the entropy generation rate for Carreau-Yasuda fluid is derived in the presence of porosity irreversibility, fluid friction irreversibility, heat transfer irreversibility and Joule heating irreversibility through second law of thermodynamics. The fluid flow is saturated and magnetized through Darcy-Forchheimer porous medium and applied magnetic field. The energy equation is modeled in the presence of viscous dissipation. Series solutions are calculated by semi analytical method HAM. The behavior of pertinent flow parameters is discussed graphically. The main interest in giving to the engineering curiosity like velocity gradient and Nusselt number. The main theme of this research communication is to enhance the information of entropy optimized flow and heat and mass transport, and to inspire the investigators and analysts to scrutinize gradually innovative attributes that can take improvement on the entropy generation minimization.

A lubricant-infused slip surface for drag reduction

Abstract: Seaweed and fish have slippery outer surfaces because of the secretion of a layer of mucus. The hydrodynamics over a three-dimensional lubricant-infused slip surface that mimics the mucus layers of seaweed and fish was numerically explored. The morphological features of the lubricant-infused surface were designed to mimic such biological mucus storage systems. The lubricant was assumed to fill the cavity and to be supplemented without limit from the bottom surface of the cavity. The slip motion at the interface between the lubricant and water was simulated by using the volume of fluid method. Simulations were performed for two cavity open area fractions, 40% and 60%, and for three lid thicknesses, 0.01D, 0.03D, and 0.06D, where D is the width of the cavity (D = 400 μm). The simulation was conducted by employing realistic material properties. The contact angle of the lubricant in deionized water was directly measured (θeq = 25.9°). This slippery lubricant layer contributes to drag reduction by lessening the velocity gradient of the surrounding fluid. The hydrodynamics of the slip surface was examined by scrutinizing the effects of varying the open area and the lid thickness on the slip velocity and length, the dispersion area, and the lubricant consumption. The maximum slip velocity and length were obtained in the center of the contact interface, which forms a paraboloid. The effects of varying the cavity open area fraction on the maximum slip velocity and length are significant. The lid thickness affects both the lubricant dispersion pattern and the height to which the lubricant builds up. The lubricant consumption for a cavity open area fraction of 60% is larger than that for 40%. The cavity with an open area fraction of 60% and a lid thickness of 0.06D provides the best drag reduction of the cavities we simulated.

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 field, measuring the magnetization of interstellar media and estimating the fraction of gravitational collapsing gas in molecular clouds using spectral line observations. In this paper, 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 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 means of 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.

Shear-induced deconfinement of hard disks

Abstract: Using Brownian dynamics simulations, we investigate the response to shear of a two-dimensional system of quasi-hard disks that are confined in the velocity gradient direction by a smooth external potential. Shearing the confined system leads to a homogenization of the one-body density profile. In order to rationalize this deconfinement effect, we split the internal one-body force field into adiabatic and superadiabatic contributions. We demonstrate that the superadiabatic force field consists of viscous and of structural contributions. We give an empirical scaling law that yields results for the superadiabatic force profiles both in the flow and in the gradient direction, in excellent agreement with the simulation data.

Coherent Structures Modulate Atmospheric Surface Layer Flux-Gradient Relationships

Abstract: Since its inception in the 1940s, Monin-Obukhov similarity theory (MOST), which relates turbulent fluxes to mean vertical gradients in the lower atmosphere, has become ubiquitous for predicting surface fluxes of quantities transported by the flow in numerical weather, climate, and hydrological forecasting models. Despite its widespread use, MOST does not account for the effects of large coherent structures in the flow, which modulate the amplitude of turbulent fluctuations, and are responsible for a large fraction of the total transport. Herein, we demonstrate that the incorporation of the large-scale streamwise velocity u_{l}(x,t)=G_{δ}⋆u(x,t), where G_{δ} is a low-pass filtering kernel, into dimensional analysis leads to an additional dimensionless parameter α(x,t), which captures the modulating influence of these structures on flux-gradient relationships. Atmospheric observations and large-eddy simulations are used to demonstrate that observed deviations from MOST can indeed be explained by this new parameter; coherent structures induce an alternating loading and unloading of the mean velocity gradient near the surface.

Advancing the Velocity Gradient Technique: Using Gradient Amplitudes and Handling Thermal Broadening

Abstract: The recent development of the Velocity Gradient Technique allows observers to map magnetic field orientations and magnetization using the direction of velocity gradients. Aside from the directions, amplitudes of velocity gradients also contain valuable information about the underlying properties of magneto-hydrodynamic (MHD) turbulence. In this paper, we explore what physical information is contained in the amplitudes of velocity gradients and discuss how this information can be used to diagnose properties of turbulence in both diffuse and self-gravitating interstellar media. We identify the relations between amplitudes of both intensity and velocity centroid gradients and the sonic Mach number $M_s$ and they are consistent with the theory's predictions. We test the robustness of the method and discuss how to utilize the amplitudes of gradients into self-gravitating media. To extend the velocity gradient technique we also discuss the usage of amplitude method to Position-Position Velocity (PPV) space as a possible way to retrieve the velocity channel maps before the contamination of thermal broadening. We discuss that the Velocity Gradient Technique with these advancements could potentially give a significantly more accurate statistical insight into the properties magnetized turbulence.

Dual solutions of nanomaterial flow comprising titanium alloy (Ti6Al4V) suspended in Williamson fluid through a thin moving needle with nonlinear thermal radiation: stability scrutinization

Abstract: Titanium alloy nanoparticle has a variety of applications in the manufacturing of soap and plastic, microsensors, aerospace design material, nano-wires, optical filters, implantation of surgical, and many biological treatments. Therefore, this research article discussed the influence of nonlinear radiation on magneto Williamson fluid involving titanium alloy particles through a thin needle. The arising system of partial differential equations is exercised by the similarity transformations to get the dimensional form of ordinary differential equations. The dual nature of solutions is obtained by implementing bvp4c. The study of stability has been carried out to check which of the results are physically applicable and stable. Influences of pertinent constraints on the flow field are discussed with the help of graphical representations and the method validation is shown in Table 1. The results imply that more than one result is established when the moving needle and the free-stream travel in the reverse directions. Moreover, the magnetic parameter accelerates the severance of boundary-layer flow, while the separation delays in the absence of the nanoparticle. The velocity gradient of nanofluid decays owing to the Williamson parameter in both branches of the outcome, while the temperature shrinks in the first or upper branch solution (stable one) and uplifts in the second or lower branch solution (unstable one). The size of the needle decreases the velocity in the upper solution and accelerates in the lower solution. The patterns of streamlines are more complicated due to the reverse direction of the free stream and thin needle.

Topology of the second-order constitutive model based on the Boltzmann–Curtiss kinetic equation for diatomic and polyatomic gases

Abstract: The topological aspects of fluid flows have long been fascinating subjects in the study of the physics of fluids. In this study, the topology of the second-order Boltzmann–Curtiss constitutive model beyond the conventional Navier–Stokes–Fourier equations and Stokes’s hypothesis was investigated. In the case of velocity shear, the topology of the second-order constitutive model was shown to be governed by a simple algebraic form. The bulk viscosity ratio in diatomic and polyatomic gases was found to play an essential role in determining the type of topology: from an ellipse to a circle, to a parabola, and then finally to a hyperbola. The topology identified in the model has also been echoed in other branches of science, notably in the orbits of planets and comets and Dirac cones found in electronic band structures of two-dimensional materials. The ultimate origin of the existence of the topology was traced to the coupling of viscous stress and velocity gradient and its subtle interplay with the bulk viscosity ratio. In the case of compression and expansion, the topology of the second-order constitutive model was also found to be governed by a hyperbola. The trajectories of solutions of two representative flow problems—a force-driven Poiseuille gas flow and the inner structure of shock waves—were then plotted on the topology of the constitutive model, demonstrating the indispensable role of the topology of the constitutive model in fluid dynamics.

Curvature of Magnetic Field Lines in Compressible Magnetized Turbulence: Statistics, Magnetization Predictions, Gradient Curvature, Modes, and Self-gravitating Media

Abstract: Magnetic field lines in interstellar media have a rich morphology, which could be characterized by geometrical parameters such as curvature and torsion. In this paper, we explore the statistical properties of magnetic field line curvature $\kappa$ in compressible magnetized turbulence. We see that both the mean and standard deviation of magnetic field line curvature obey power-law relations to the magnetization. Moreover, the power-law tail of the curvature probability distribution function is also proportional to the Alfvenic Mach number. We also explore whether the curvature method could be used in the field-tracing Velocity Gradient Technique. In particular, we observe that there is a relation between the mean and standard deviation of the curvature probed by velocity gradients to $M_A$. Finally we discuss how curvature is contributed by different MHD modes in interstellar turbulence, and suggests that the eigenvectors of MHD modes could be possibly represented by the natural Fernet-Serrat frame of the magnetic field lines. We discuss possible theoretical and observational applications of the curvature technique, including the extended understanding on a special length scale that characterize the importance of magnetic field curvature in driving MHD turbulence, and how it could be potentially used to study self-gravitating system.

Internal flows of ventilated partial cavitation

Abstract: Our study provides the first experimental investigation of the internal flows of ventilated partial cavitation (VPC) formed by air injection behind a backward-facing step. The experiments are conducted using flow visualization and planar particle image velocimetry with fog particles for two different cavity regimes of VPC, i.e., open cavity (OC) and two-branch cavity (TBC), under various ranges of free stream velocity (U) and ventilation rates (Q). Our experiments reveal similar flow patterns for both OC and TBC, including forward flow region near the air–water interface, reverse flow region, near-cavitator vortex, and internal flow circulation vortex. However, OC internal flow exhibits highly unsteady internal flow features, while TBC internal flow shows laminar-like flow patterns with a Kelvin–Helmholtz instability developed at the interface between forward and reverse flow regions within the cavity. Internal flow patterns and the unsteadiness of OC resemble those of turbulent flow separation past a backward-facing step (BFS flow), suggesting a strong coupling of internal flow and turbulent external recirculation region for OC. Likewise, internal flow patterns of TBC resemble those of laminar BFS flow, with the presence of unsteadiness due to the strong velocity gradient across the forward–reverse flow interface. The variation in the internal flow upon changing U or Q is further employed to explain the cavity regime transition and the corresponding change of cavity geometry. Our study suggests that the ventilation control can potentially stabilize the cavity in the TBC regime by delaying its internal flow regime transition from laminar-like to highly unsteady.

Capturing Velocity Gradients and Particle Rotation Rates in Turbulence.

Abstract: Turbulent fluid flows exhibit a complex small-scale structure with frequently occurring extreme velocity gradients. Particles probing such swirling and straining regions respond with an intricate shape-dependent orientational dynamics, which sensitively depends on the particle history. Here, we systematically develop a reduced-order model for the small-scale dynamics of turbulence, which captures the velocity gradient statistics along particle paths. An analysis of the resulting stochastic dynamical system allows pinpointing the emergence of non-Gaussian statistics and nontrivial temporal correlations of vorticity and strain, as previously reported from experiments and simulations. Based on these insights, we use our model to predict the orientational statistics of anisotropic particles in turbulence, enabling a host of modeling applications for complex particulate flows.