Standard Fluid Model Research Articles

Impact of magnetized nanoparticle aggregation over a Riga plate with thermal radiation in water‐Al2O3 based nanofluid flow

AbstractThe nanoparticle (NP) volume fraction is a critical variable in fluid models, including the Brinkman, Einstein, and Maxwell designs. The temperature does not affect the nanofluid's normalized shear viscosity. The aggregation model elucidates such traits. Furthermore, the experimental results show a larger increase in the thermal conductivity of nano liquids than the values obtained using standard fluid models. The impact of nanoparticle aggregation (NPAgs) is ignored, which contributes to the disparity. Therefore, it is essential to study the thermal conductivity ratio while considering the kinematics of NPAgs. Therefore, the radiation impact is investigated here by examining NPAgs on the Riga surface in the context of a porous media. The circulation and temperature governing equations are transformed using suitable similarity variables into ordinary differential equations (ODEs). The Runge‐Kutta‐Fehlberg 4‐5 order (RKF‐45) and shooting method is used to simplify the resulting equations numerically. The graphic representation illustrates the influence of many non‐dimensional factors on significant physical quantities. The velocity of the nanofluid has a positive correlation with the modified Hartmann number, whereas it demonstrates a negative correlation with the porosity parameter. A better thermal distribution occurs with higher levels of radiation constraint. The inclusion of a higher solid volume percentage results in a decrease in the velocity profile while concurrently improving the thermal distribution. It is worth noting that NPs that exhibit aggregation have a more prominent thermal distribution than those that do not aggregate, results in greater rate of thermal distribution in the former scenario. The present investigation outcomes will useful in advanced cooling systems, improving energy efficiency, material, environmental and biomedical engineering.

Dynamic evolutions of Bohm sheaths and pre-sheaths

The time evolutions of the Bohm sheath and the related pre-sheath are analyzed as an initial value problem. The standard classical fluid model of a collisionless plasma is used with cold ions and Boltzmann distributed electrons. Numerical solutions of the basic equations show that a stationary plasma sheath itself is established within a few ion plasma periods. It is demonstrated analytically that for infinitely extended homogeneous plasmas in one spatial dimension, the only possible pre-sheath solution is dynamic, giving a steady expansion: no stationary solution exists for this one-dimensional case. The potential and density drops along the dynamic pre-sheath differ notably from the values found for stationary models suggested in the literature. Collisions give only formal changes to the collisionless results, and their substance remains the same in one spatial dimension. Cylindrical and spherical geometries, on the other hand, allow for physically acceptable, fully nonlinear, stationary solutions with analytical results given. These are supported by numerical solutions.

Second law assessment of injected nanoparticles to blood flow with thermal radiation and magnetic field in conduit artery

BackgroundThe stipulated flow over an artery is optimized by adopting an artery as convergent or divergent channel with an arbitrary cross section. The standard Carreau fluid Model is used in this work to account for viscoelasticity in the whole network. The viscoelastic contribution at borders (inlet, outlet, and core region) is implemented while keeping the mathematical model parabolic character in mind. Due to low toxicity, MgO nanoparticles dispersed in blood having potent antibacterial effects against three major food-borne illnesses. Furthermore, Hypomagnesaemia is produced by a magnesium deficit in the blood, which is an additional stimulation for different diseases such as diarrhea, nausea, and decrease in appetite. To compensate for this shortage, MgO is delivered as a nanoparticle into the blood (base fluid). The mechanics of energy and irreversibility are evaluated with the contribution of viscous dissipation, Ohmic heating, and radiant heat. MethodsSuitable renovations are used to amend the system of complex PDEs into nonlinear ODEs. The numerical solutions to these ODEs are calculated using the fourth order Runge-Kutta scheme and the shooting mechanism. Significant findingAn elevation of radiation parameter contributes significantly to blood velocity, temperature, and entropy. The flow dynamic and energy of the blood stream is higher when nanoparticles are injected in base fluid. Bejan detracts as Brinkman number grows but increases as radiation parameter increases. High Weissenberg numbers dictate thermodynamic behavior relating to pure elastic energy. The system entropy amplifies against Rd. With increase in M, viscous dissipation irreversibility takes precedence overheat transfer irreversibility, while Be deteriorate.

Numerical and experimental study of influence function in magnetorheological finishing (MRF) of freeform surface

In the present work, a dynamic viscosity model is proposed based on the varying magnetic flux density of the neodymium permanent magnet along its width. The proposed viscosity model is helpful in analysing the influence function in a better way as compared to standard non-Newtonian fluid models. During the finishing process, the research of influence function aids in establishing the right range of process parameters. MR fluid flow on the freeform surface is examined numerically and experimentally to better understand the influence function. The flow behaviour of the MR fluid is investigated using the three-dimensional (3D) computational fluid dynamics (CFD) simulation, wall shear stress and dynamic pressure are estimated on the Oxygen-free high conductivity (OFHC) copper for various process parameters (working gap and rotational speed). On the convex and concave sections of a freeform surface, indentation depth is estimated for various process parameters using the results of dynamic pressure and empirical relation. Finishing tests are performed to investigate forces (tangential and normal) and indentation depth on the workpiece, and the results are evaluated.

Nanoindentation study of the viscoelastic properties of human triple negative breast cancer tissues: Implications for mechanical biomarkers.

This paper presents the results of a combined experimental and theoretical study of the structure and viscoelastic properties of human non-tumorigenic mammary breast tissues and triple negative breast cancer (TNBC) tissues of different histological grades. A combination of immunofluorescence and confocal microscopy, and atomic force microscopy is used to study the actin cytoskeletal structures of non-tumorigenic and tumorigenic breast tissues (grade I to grade III). A combination of nanoindentation and statistical techniques is then used to measure viscoelastic properties of non-tumorigenic and human TNBC of different histological grades. A Standard Fluid Model/Anti-Zener Model II is also used to characterize the viscoelastic properties of the non-tumorigenic and tumorigenic TNBC tissues of different grades. The implications of the results are discussed for the potential application of nanoindentation and statistical deconvolution techniques to the development of mechanical biomarkers for TNBC detection/cancer diagnosis. STATEMENT OF SIGNIFICANCE: There is increasing interest in the development of mechanical biomarkers for cancer diagnosis. Here, we show that nanoindentation techniques can be used to characterize the viscoelastic properties of normal breast tissue and TNBC tissues of different histological grades. The Standard Fluid Model (Anti-Zener Model II) is used to classify the viscoelastic properties of breast tissues of different TNBC histological grades. Our results suggest that breast tissue and TNBC tissue viscoelastic properties can be used as mechanical biomarkers for the detection of TNBC at different stages.

Macroscopic plasma analysis from 1D-radial kinetic results of a Hall thruster discharge

A radial particle-in-cell model of the weakly-collisional plasma discharge in a Hall thruster, provides the non-Maxwellian velocity distribution functions (VDF) of ions and electrons. The model considers a radial magnetic field, secondary electron emission from the two walls, and phenomenological models of anomalous electron scattering. The electron VDF is used to assess the different terms in the macroscopic momentum and energy equations, identifying those differing from the standard fluid model for a near-Maxwellian VDF. The pressure tensor consists of an anisotropic gyrotropic part and a small gyroviscous part. Nonetheless, the gradient of this last one affects the cross-field electron current density, generating radial undulations that resemble those reported for near-wall conductivity. A gyroviscous energy flux is identified too. The heat flux parallel to the magnetic lines does not follow a conductive-type law but a convective-type one, already found in other weakly-collisional plasmas. The tails of the electron velocity distribution function are partially depleted due to wall collection, leading to reduced electron fluxes of particles and energy, which are characterized with parameters useful for fluid models. Differences in the plasma response for annular and planar channel geometries are highlighted. The levels of replenishment of the electron VDF and of the asymmetries in radial profiles differ for isotropic and anisotropic anomalous scattering models.

Interaction between runaway electrons and internal kink in a post-disruption plasma

Direct interactions between the n = 1 (n is the toroidal mode number) resistive internal kink instability and relativistic runaway electrons (REs) in a post thermal quench toroidal plasma are numerically investigated. A recently developed hybrid model, where the runaway current is treated as a fluid component, is adopted to study how REs affect the internal kink stability and the associated eigenmode structure. The RE-modified internal kink perturbation is in turn superposed with the equilibrium field, in order to study the effects of 3D fields on the drift orbits of REs and consequently on the RE confinement and loss. Results are compared with that assuming the single fluid model for the runaway beam. It is found that REs destabilize the resistive internal kink mode, leading to a better recovery (compared to the standard single fluid model) of the mode growth rate scaling of γ ∼ S −1/3 at lower values of Lundquist number S. Furthermore, REs significantly modify the internal kink eigenfunction inside or near the q = 1 surface. In particular, a new narrow layer forms within the resistive layer, where a strong peaking of the perturbed parallel current develops. The RE contribution is also found to substantially enhance the coupling among poloidal harmonics, in particular between m = 1 and its nearest sidebands. All these changes to the perturbation structure consequently affect the RE drift orbits in the presence of the internal kink instability. Compared to the fluid model, 3D perturbations computed with the more consistent hybrid model lead to less loss of relativistic electrons in the RE beam, when the perturbation level reaches that of the equilibrium field. At lower (but still large) perturbation amplitude (∼10% of the equilibrium field), the internal kink mode has little effect on the RE loss. REs launched within the q = 1 surface always stay confined within the plasma, independent of the field perturbation amplitude (up to the level of the equilibrium field), the beam model adopted (fluid versus hybrid), or the particle traveling direction. On the other hand, the individual drift orbit trajectory is qualitatively sensitive to these factors.

Simulations of plasmas and fluids using anti-symmetric models

ALMA (Anti-symmetric, Large-Moment, Accelerated) is a fast, flexible, and scalable toolkit designed to solve hyperbolic conservation law systems in hybrid supercomputers. This manuscript describes the theoretical background and implementation of ALMA, which uses the anti-symmetric formulation of fluids to obtain simple, robust, and easily paralellizable code. Practical GPU acceleration is realized on entire applications with an overall gain factor of 2 to 4. ALMA also provides a parallel, GPU accelerated sparse solver based on geometric multigrid, capable of diagonalizing linear systems with 239 unknowns. We demonstrate ALMA's scaling and performance in petascale supercomputers and use standard fluid models to verify the overall approach with canonical benchmark problems.

Prediction of Fluid Behavior Using Generalized Hydraulic Calculation Method in Hydraulic Fractures

Hydraulic fracturing has been used as one of the stimulation techniques to economically increase oil and gas production by creating small cracks in subsurface geologic formations to allow oil or gas to move toward a producing well. Hydraulics plays a vital role in many oil field operations including drilling, completion, fracturing and production. In the case of fracturing, however, the role of hydraulics becomes important since optimized hydraulics can minimize the cost and conversely, any miscalculations may cause problems such as the fluid loss or may potentially even lead to loss of the well. The current methods of the hydraulic calculation for non-Newtonian fluids necessitate determination of the robust model. This paper presented a new method for calculating pressure losses in the hydraulic fractures. The objective of this study was to develop the generalized model for hydraulic calculation for non-Newtonian fluid and run the case studies for the model validation. In the present work, detailed algorithm for the hydraulic calculation has been developed and then programmed in C++. The only input to the program is the raw rheological data, shear stress versus shear rate and the geometrical characteristics of the slit. Model validation with the new method has established a very small percentage difference between the values predicted by the model and experimental data. The results demonstrate that the new method is accurately predicting the pressure drop in both laminar and turbulent flow regimes. It is shown that the fluid behavior is more accurately represented using the new method than that with the standard fluid models available in the petroleum industry. Further validation and development to be carried out using experimental data for variety of fluid types.

Fractional viscoelastic modelling of wave propagation in fluid-saturated marine sediments

It is shown that Buckingham's grain-shearing (GS) model [JASA (2000)] as well as its improved viscous-GS (VGS) model [JASA (2007)] can be expressed using the mathematical framework of fractional calculus. The fractional version of the standard fluid model is adopted to independently arrive at the wave equations and dispersion relations derived by Buckingham. The fractional-order wave equations obtained for the compressional waves and shear waves are relatively easier to analyse due to their closed-form representation in the fractional framework. It is also shown that the fractional calculus approach may help in bridging the disparate fields of non-Newtonian rheology and sediment acoustics, which may have actually developed independently of each other. Further, the experimental data relating wave dispersion and attenuation in marine sediments is found to match with the predictions from the fractional framework. The overall goal is to show that fractional calculus is not just a mathematical framework that can only be applied to curve-fit the observational data for complex media. In fact, it has an inherent connection to real physical processes that needs to be explored more.

A multi-scale model for simulating liquid-fabric interactions

We propose a method for simulating the complex dynamics of partially and fully saturated woven and knit fabrics interacting with liquid, including the effects of buoyancy, nonlinear drag, pore (capillary) pressure, dripping, and convection-diffusion. Our model evolves the velocity fields of both the liquid and solid relying on mixture theory, as well as tracking a scalar saturation variable that affects the pore pressure forces in the fluid. We consider the porous microstructure implied by the fibers composing individual threads, and use it to derive homogenized drag and pore pressure models that faithfully reflect the anisotropy of fabrics. In addition to the bulk liquid and fabric motion, we derive a quasi-static flow model that accounts for liquid spreading within the fabric itself. Our implementation significantly extends standard numerical cloth and fluid models to support the diverse behaviors of wet fabric, and includes a numerical method tailored to cope with the challenging nonlinearities of the problem. We explore a range of fabric-water interactions to validate our model, including challenging animation scenarios involving splashing, wringing, and collisions with obstacles, along with qualitative comparisons against simple physical experiments.

Testing the role of molecular physics in dissipative divertor operations through helium plasmas at DIII-D

Recent experiments in DIII-D helium plasmas are examined to resolve the role of atomic and molecular physics in major discrepancies between experiment and modeling of dissipative divertor operation. Helium operation removes the complicated molecular processes of deuterium plasmas that are a prime candidate for the inability of standard fluid models to reproduce dissipative divertor operation, primarily the consistent under-prediction of radiated power. Modeling of these experiments shows that the full divertor radiation can be accounted for, but only if measures are taken to ensure that the model reproduces the measured divertor density. Relying on upstream measurements instead results in a lower divertor density and radiation than is measured, indicating a need for improved modeling of the connection between the divertor and the upstream scrape-off layer. These results show that fluid models are able to quantitatively describe the divertor-region plasma, including radiative losses, and indicate that efforts to improve the fidelity of the molecular deuterium models are likely to help resolve the discrepancy in radiation for deuterium plasmas.

Monte-Carlo fluid approaches to detached plasmas in non-axisymmetric divertor configurations

Fluid transport modeling in three-dimensional boundaries of toroidal confinement devices is reviewed with the emphasis on a Monte-Carlo approach to simulate detached plasmas. The loss of axisymmetry in such configurations presents a major challenge for numerical implementation of the standard fluid model widely applied to fusion experimental devices. A large-scale effort has been made to address this problem under complementary aspects including different magnetic topologies and numerical techniques. In this paper, we give a brief review of the different strategies pioneered and the challenges involved. A more detailed description is provided for the Monte-Carlo code—EMC3-Eirene, where the physics model and the basic idea behind the applied Monte-Carlo method are presented. The focus is put on its applications to detachment studies for stellarators and tokamaks. Here, major achievements and difficulties encountered are described. Model limitations and further development plans are discussed.

Coarse-grained cosmological perturbation theory: Stirring up the dust model

We study the effect of coarse graining the dynamics of a pressureless self-gravitating fluid (coarse-grained dust) in the context of cosmological perturbation theory, in both the Eulerian and Lagrangian frameworks. We obtain recursion relations for the Eulerian perturbation kernels of the coarse-grained dust model by relating them to those of the standard pressureless fluid model. The effect of the coarse graining is illustrated by means of power and cross spectra for the density and velocity, which are computed up to one-loop order. In particular, the large-scale vorticity power spectrum that arises naturally from a mass-weighted velocity is derived from first principles. We find qualitatively good agreement for the magnitude, shape, and spectral index of the vorticity power spectrum with recent measurements from $N$-body simulations and results from the effective field theory of large-scale structure. To lay the ground for applications in the context of Lagrangian perturbation theory, we finally describe how the kernels obtained in Eulerian space can be mapped to Lagrangian ones.

Electron kinetics inferred from observations of microwave bursts during edge localized modes in the mega-amp spherical tokamak.

Recent measurements of microwave and x-ray emission during edge localized mode (ELM) activity in tokamak plasmas provide a fresh perspective on ELM physics. It is evident that electron kinetics, which are not incorporated in standard (fluid) models for the instability that drives ELMs, play a key role in the new observations. These effects should be included in future models for ELMs and the ELM cycle. The observed radiative effects paradoxically imply acceleration of electrons parallel to the magnetic field combined with rapid acquisition of perpendicular momentum. It is shown that this paradox can be resolved by the action of the anomalous Doppler instability which enables fast collective radiative relaxation, in the perpendicular direction, of electrons accelerated in the parallel direction by inductive electric fields generated by the initial ELM instability.

Modelling of tokamak glow discharge cleaning I: physical principles

Glow discharge cleaning (GDC) is a common technique for the conditioning of tokamak vessel walls in order to improve plasma performance and will be one of the primary conditioning techniques in ITER. The GDC discharge is a dc low-temperature plasma discharge, operated in the absence of the toroidal magnetic field, between one or more anodes inserted into the vessel, and the entire vessel wall serving as a cathode. This paper presents a self-consistent 2D model of the GDC discharge with the aim of improving fundamental understanding and predicting the wall ion current density distribution in ITER. The model combines a standard fluid model of the quasineutral plasma bulk with non-standard fluid equations for the fast electrons accelerated by the cathode sheath, based on transport coefficients and rate coefficients deduced from a Monte Carlo simulation. Examples of model results are shown in order to illustrate the general principles of the GDC discharge and the influence of the model input parameters. An important insight gained from this work is that the GDC discharge operates basically as a hollow-cathode discharge: the plasma is sustained mainly by ionization by secondary electrons emitted from the cathode, accelerated ballistically through a thin cathode sheath, penetrating the plasma as a fast electron beam, and trapped by the cathode fall surrounding the plasma on all sides. The electric field distribution inside the plasma, which determines the ion flux distribution on the vessel walls, is controlled by low-energy plasma bulk electrons. The relatively small surface area of the anode leads to the formation of an anode glow affecting the plasma uniformity. Comparisons with experimental data and predictions for ITER are presented in a companion paper.

Beyond single-stream with the Schrödinger method

AbstractWe investigate large scale structure formation of collisionless dark matter in the phase space description based on the Vlasov-Poisson equation. We present the Schrödinger method, originally proposed by \cite{WK93} as numerical technique based on the Schrödinger Poisson equation, as an analytical tool which is superior to the common standard pressureless fluid model. Whereas the dust model fails and develops singularities at shell crossing the Schrödinger method encompasses multi-streaming and even virialization.

Parallel implementation of isothermal and isoenergetic Dissipative Particle Dynamics using Shardlow-like splitting algorithms

A parallel implementation of the Shardlow splitting algorithm (SSA) for Dissipative Particle Dynamics (DPD) simulations is presented. The isothermal and isoenergetic SSA implementations are compared to the DPD version of the velocity-Verlet integrator in terms of numerical stability and performance. The integrator stability is assessed by monitoring temperature, pressure and total energy for both the standard and ideal DPD fluid models. The SSA requires special consideration due to its recursive nature resulting in more inter-processor communication as compared to traditional DPD integrators. Nevertheless, this work demonstrates that the SSA exhibits stability over longer time steps that justify its regular use in parallel, multi-core applications. For the computer architecture used in this study, a factor of 10–100 speedup is achieved in the overall time-to-solution for isoenergetic DPD simulations and a 15–34 speedup is achieved for the isothermal DPD simulations.

Quantum vortex dynamics under the tangent representation of the local induction approximation

AbstractWe derive the local induction approximation (LIA) for a quantum vortex filament in the arclength coordinate frame where the tangent vector is the unknown function. The equation for the tangent vector to the filament is then converted to a potential form, which ends up being a type of nonlinear Schrödinger equation that governs the tangential LIA model (T-LIA). Such a formulation was previously derived by Umeki for the standard fluid model (in the absence of superfluid friction terms). While it is challenging to generalize many of the exact solutions found for the standard LIA to the quantum LIA model, we demonstrate that the T-LIA model facilitates this generalization nicely. Indeed, under the T-LIA model, we are able to construct a variety of solutions. The Hasimoto solution related to elastica is one of the fundamental solutions present for the standard fluid model; however, using the T-LIA model, we are able to demonstrate the existence of such a solution, thereby extending the Hasimoto solution to the superfluid case. In the zero-temperature limit, purely self-similar solutions are shown to exist for the T-LIA model. As the superfluid warms (so that the influence of the normal flow is no longer negligible), the analogue to the self-similar solution is a new class of solutions, which depend on the similarity variable as well as a time-dependent additive scaling. In other words, the self-similar structures gradually deform as the magnitude of the normal-fluid velocity increases, which makes complete physical sense. When dealing with small deviations from the central axis of alignment, we can describe such solutions analytically. There exists a family of helical vortex filaments in the presence of a normal fluid impinging on the vortex, in complete agreement with the previously studied results for the LIA model. Finally, a number of soliton solutions are shown to exist in different regimes of the T-LIA model.

The impact of kinetic effects on the properties of relativistic electron–positron shocks

We assess the impact of non-thermally shock-accelerated particles on the magnetohydrodynamic (MHD) jump conditions of relativistic shocks. The adiabatic constant is calculated directly from first-principles particle-in-cell simulation data, enabling a semi-kinetic approach to improve the standard fluid model and allowing for an identification of the key parameters that define the shock structure. We find that the evolving upstream parameters have a stronger impact than the corrections due to non-thermal particles. We find that the decrease in the upstream bulk speed result in deviations from the standard MHD model up to 10%. Furthermore, we obtain a quantitative definition of the shock transition region from our analysis. For Weibel-mediated shocks the inclusion of a magnetic field in the MHD conservation equations is addressed for the first time.