Momentum Diffusion Research Articles

Flow of ferrofluid within a channel driven by a rotating magnetic field: Implications of surface magnetic stresses and magnetic body couples

This research presents a discussion of the flow of a ferrofluid in a square cross-sectional area channel driven by a rotating magnetic field. The objective was to evaluate the coupled effect of surface magnetic stresses and diffusion of the internal angular momentum as potential mechanisms for generating flow. In many analyses of flow induced by time-dependent magnetic fields, the effect of the diffusion of the internal angular momentum has been dismissed, based on the negligible value of the spin viscosity coefficient estimated from order-of-magnitude analyses. In light of these considerations, we conducted a review of the existing analyses and put forward a new approach of the order-of-magnitude analysis of the spin viscosity coefficient. The paper presents a detailed description of the solution procedure for the flow field, with and without the inclusion of the diffusion of the internal angular momentum. To justify the assumptions involved in the analytical solution of the flow, we expanded a previous scale analysis to define Reynolds and Strouhal numbers in the linear and internal angular momentum balance equations. It was proven that the maximum surface velocity predicted at the ferrofluid–air boundary closely aligns with the reported experimental data for moderate amplitudes of the magnetic field.

Growth of thermoplastic shear band

Shear localization is a fundamental and widely observed non-equilibrium phenomenon in metallic materials subjected to impulsive loadings. Despite extensive research over several decades, the evolution of shear bands still remains poorly understood. In this study, we propose a two-stage model to describe the evolution of thermoplastic shear band, where the effects of strain hardening, strain-rate hardening, and thermal softening are involved. Our analysis reveals that the growth of thermoplastic shear band is derived by the competition between momentum diffusion and thermal diffusion processes, which is controlled by the solid-state equivalent of the Prandtl number. By incorporating these factors into our model, we find that the presence of hardening effect retards the evolution of shear bands, resulting in a wider shear band and increased dissipation of energy. Theoretical calculation results of shear bandwidth, shear band strain, propagation velocity, process zone geometry and dimensions, critical dissipation energy, shear band toughness, and shear band spacing are well consistent with available experimental data. Additionally, we explore the potential transition to turbulence controlled by Reynolds number within shear bands and investigate the influence of the Taylor-Quinney coefficient on the evolution of shear bands. These findings are expected to offer valuable insights into the mechanism of shear band evolution.

Improving approximation accuracy in Godunov-type smoothed particle hydrodynamics methods

The study examines the origin of errors resulting from the approximation of the right hand sides of the Euler equations using the Godunov type contact method of smoothed particle hydrodynamics (CSPH). The analytical expression for the numerical shear viscosity in CSPH method is obtained. In our recent study the numerical viscosity was determined by comparing the numerical solution of momentum diffusion in the shear flow with theoretical one. In this study we deduce the analytical expression for the numerical viscosity which is found to be similar to numerical one, confirming the obtained results. To reduce numerical diffusion, diffusion limiters are typically applied to expressions for contact values of velocity and pressure, as well as higher-order reconstruction schemes. Based on the performed theoretical analysis, we propose a new method for correcting quantities at interparticle contacts in CSPH method, which can be easily extended to the MUSCL-type (Monotonic Upstream-centered Scheme for Conservation Laws) method. Original CSPH and MUSCL-SPH approaches and ones with aforementioned correction are compared.

Application of roughness models to stationary and rotating minichannel flows

PurposeThe performance of a bladeless Tesla turbine is closely tied to momentum diffusion, kinetic energy transfer and wall shear stress generation on its rotating disks. The surface roughness adds complexity of flow analysis in such a domain. This paper aims to assess the effect of roughness on flow structures and the application of roughness models in flow cross sections with submillimeter height, including both stationary and rotating walls.Design/methodology/approachThis research starts with the examination of flow over a rough flat plate, and then proceeds to study flow within minichannels, evaluating the effect of roughness on flow characteristics. An in-house test stand validates the numerical solutions of minichannel. Finally, flow through the minichannel with corotating walls was analyzed. The k-ω SST turbulent model and Aupoix's roughness method are used for numerical simulations.FindingsThe findings emphasize the necessity of considering the constricted dimensions of the flow cross section, thereby improving the alignment of derived results with theoretical estimations. Moreover, this study explores the effects of roughness on flow characteristics within the minichannel with stationary and rotating walls, offering valuable insights into this intricate phenomenon, and depicts the appropriate performance of chosen roughness model in studied cases.Originality/valueThe originality of this investigation is the assessment and validation of flow characteristics inside minichannel with stationary and corotating walls when the roughness is implemented. This phenomenon, along with the effect of roughness on the transportation of kinetic energy to the rough surface of a minichannel in an in-house test setup, is assessed.

Extended analytical model of Tesla turbine with advanced modelling of velocity profile in minichannel between corotating disks with consideration of surface roughness

Consideration of roughness effects in the flow in a minichannel has been a major scientific problem for many decades. Roughness can alter the momentum diffusion, heat transfer conditions or laminar-turbulent transition. These effects are even more pronounced in minichannel flows where the roughness can occupy a large part of the cross-section. Modelling methods applied so far usually fall short in internal flows with high relative roughness. The presented paper pertains to the analytical flow model in Tesla turbine components with consideration of roughness on the rotor walls. The model uses the equivalent sand grain approach to modify dynamic viscosity in the governing equations to achieve a desired downward shift of the dimensionless velocity profile. The model solves two-dimensional equations of continuity, momentum and energy. The semi-empirical function was derived to consider the change in the shape of the radial velocity. The applied model incorporates Euler's turbomachinery equation to determine the influence of roughness on the turbine performance under varied operating conditions. Roughness shortens the streamlines inside the rotor, but the overall turbine's performance is improved. The roughness equal to 10−5 m increased the power generated and isentropic efficiency by factors of 3 and 2.5, respectively, compared to the smooth rotor.

Large eddy simulations of flow over additively manufactured surfaces: Impact of roughness and skewness on turbulent heat transfer

Additive manufacturing creates surfaces with random roughness, impacting heat transfer and pressure loss differently than traditional sand–grain roughness. Further research is needed to understand these effects. We conducted high-fidelity heat transfer simulations over three-dimensional additive manufactured surfaces with varying roughness heights and skewness. Based on an additive manufactured Inconel 939 sample from Siemens Energy, we created six surfaces with different normalized roughness heights, Ra/D=0.001,0.006,0.012,0.015,0.020, and 0.028, and a fixed skewness, sk=0.424. Each surface was also flipped to obtain negatively skewed counterparts (sk=−0.424). Simulations were conducted at a constant Reynolds number of 8000 and with temperature treated as a passive scalar (Prandtl number of 0.71). We analyzed temperature, velocity profiles, and heat fluxes to understand the impact of roughness height and skewness on heat and momentum transfer. The inner-scaled mean temperature profiles are of larger magnitude than the mean velocity profiles both inside and outside the roughness layer. This means, the temperature wall roughness function, ΔΘ+, differs from the momentum wall roughness function, ΔU+. Surfaces with positive and negative skewness yielded different estimates of equivalent sand–grain roughness for the same Ra/D values, suggesting a strong influence of slope and skewness on the relationship between roughness function and equivalent sand–grain roughness. Analysis of the heat and momentum transfer mechanisms indicated an increased effective Prandtl number within the rough surface in which the momentum diffusivity is larger than the corresponding thermal diffusivity due to the combined effects of turbulence and dispersion. Results consistently indicated improved heat transfer with increasing roughness height and positively skewed surfaces performing better beyond a certain roughness threshold than negatively skewed ones.

The Role of Turbulence in an Intense Tropical Cyclone: Momentum Diffusion, Eddy Viscosities, and Mixing Lengths

Abstract Improved representation of turbulent processes in numerical models of tropical cyclones (TCs) is expected to improve intensity forecasts. To this end, the authors use a large-eddy simulation (with 31-m horizontal grid spacing) of an idealized category 5 TC to understand the role of turbulent processes in the inner core of TCs and their role on the mean intensity. Azimuthally and temporally averaged budgets of the momentum fields show that TC turbulence acts to weaken the maximum tangential velocity, diminish the strength of radial inflow into the eye, and suppress the magnitude of the mean eyewall updraft. Turbulent flux divergences in both the vertical and radial directions are shown to influence the TC mean wind field, with the vertical being dominant in most of the inflowing boundary layer and the eyewall (analogous to traditional atmospheric boundary layer flows), while the radial becomes important only in the eyewall. The validity of the downgradient eddy viscosity hypothesis is largely confirmed for mean velocity fields, except in narrow regions which generally correspond to weak gradients of the mean fields, as well as a narrow region in the eye. This study also provides guidance for values of effective eddy viscosities and vertical mixing length in the most turbulent regions of intense TCs, which have rarely been measured observationally. A generalized formulation of effective eddy viscosity (including the Reynolds normal stresses) is presented. Significance Statement This study uses a turbulence-resolving simulation of a category 5 tropical cyclone to understand the role of turbulence in intense storms. Results show that turbulence clearly modulates storm structure and intensity. This study provides guidance for the values of turbulent quantities (which are usually parameterized in comparatively coarse operational TC forecast models) in scarcely observed regions of intense storms. Furthermore, a complete formulation of the effective eddy viscosities is proposed, incorporating contributions from typically ignored Reynolds normal stress terms.

Calcium carbonate crystallization process analysis on a heat transfer surface

This paper explores the growth process of calcium carbonate crystallization fouling on a heat surface using finite element methods to solve physical equations such as momentum, energy, and concentration diffusion, incorporating the impact of bulk crystallization on the concentration of scaling ions. The simulation uses deformation geometry, moving grids, and automatic re-meshing methods to study the dynamic growth of fouling layers and the spatiotemporal changes in fluid velocity, temperature, and concentration field-related parameters caused by it. Results indicate that the deposition interface temperature increases along the flow direction under constant heat flux conditions, leading to an increase in deposition rate. When the interface temperature exceeds 340 K, the fouling deposition rate becomes highly sensitive to temperature changes. The fouling thickness also increases along the flow direction, causing the heat transfer surface near the outlet to face a more severe heat transfer deterioration caused by scaling. Under constant temperature conditions, the deposition rate increases rapidly near the inlet and varies less along the flow direction. When the wall temperature remains constant, scaling is more likely to occur at the fluid inlet as the fluid temperature increases. This model also examines the effects of changes in the porosity of the fouling layer and ion interactions in composite salt solutions on the growth characteristics of the fouling layer.

Collapse of neutrino wave functions under Penrose gravitational reduction

Models of spontaneous wave function collapse have been postulated to address the measurement problem in quantum mechanics. Their primary function is to convert coherent quantum superpositions into incoherent ones, with the result that macroscopic objects cannot be placed into widely separated superpositions for observably prolonged times. Many of these processes will also lead to loss of coherence in neutrino oscillations, producing observable signatures in the flavor profile of neutrinos at long travel distances. The majority of studies of neutrino oscillation coherence to date have focused on variants of the continuous state localization model, whereby an effective decoherence strength parameter is used to model the rate of coherence loss with an assumed energy dependence. Another class of collapse models that have been proposed posit connections to the configuration of gravitational field accompanying the mass distribution associated with each wave function that is in the superposition. A particularly interesting and prescriptive model is Penrose’s description of gravitational collapse which proposes a decoherence time τ determined through Egτ∼ℏ, where Eg is a calculable function of the Newtonian gravitational potential. Here we explore application of the Penrose collapse model to neutrino oscillations, reinterpreting previous experimental limits on neutrino decoherence in terms of this model. We identify effects associated with both spatial collapse and momentum diffusion, finding that the latter is ruled out in data from the IceCube South Pole Neutrino Observatory so long as the neutrino wave packet width at production is σν,x≤2×10−12 m. Published by the American Physical Society 2024

A robust and well-balanced finite volume solver for investigating the effects of tides on water renewal timescale in the Nador lagoon, Morocco

Coastal lagoons, particularly those not well-connected to the sea, are highly susceptible to continuous water retention, adversely affecting water quality and ecosystems. Understanding and quantifying the processes governing water renewal in such semi-enclosed regions is crucial. Using the principles of constituent-oriented age and residence time theory (www.climate.be/cart), we calculated timescales to explain the water renewal process in semi-enclosed areas. To improve our understanding and define the dynamics of the Nador lagoon, we use two distinct time scales: residence time and exposure time. Residence time indicates the length of time a parcel of water leaves the region of interest for the first time, while exposure time represents the overall length of time a parcel of water remains in that region, including any subsequent inflows. The modeling system adopts an Eulerian approach, including two interlinked model components: the shallow-water equations incorporating bottom friction, eddy viscosity, wind shear stresses, momentum diffusion, and Coriolis forces for modeling hydrodynamics, and a transport-diffusion equation utilized to simulate the advection and diffusion of the passive tracer concentration. The entire system is integrated into a high-order finite volume solver that employs unstructured meshes, upwind numerical fluxes, and slope limiters to achieve precise resolution of steep bathymetric gradients that may arise in the approximate solution. The scheme is non-oscillatory and preserves the conservation properties. In this research, we explore various situations related to the connection between the Mediterranean Sea and the Nador lagoon. Specifically, we suggest novel entry points that have the potential to significantly decrease the water residence within the lagoon.

Shakhov-type extension of the relaxation time approximation in relativistic kinetic theory and second-order fluid dynamics

We present a relativistic Shakhov-type generalization of the Anderson-Witting relaxation time model for the Boltzmann collision integral to modify the ratio of momentum diffusivity to thermal diffusivity. This is achieved by modifying the path on which the single particle distribution function fk approaches local equilibrium f0k by constructing an intermediate Shakhov-type distribution fSk similar to the 14-moment approximation of Israel and Stewart. We illustrate the effectiveness of this model in case of the Bjorken expansion of an ideal gas of massive particles and the damping of longitudinal waves through an ultrarelativistic ideal gas.

In-cylinder flow evolution in the horizontal plane of a motoring compression ignition engine

This study used the two-dimensional particle image velocimetry technique to quantify the in-cylinder horizontal plane velocity field evolution in a swirl-supported light-duty single-cylinder diesel engine. The data were acquired at a constant engine speed of 1600 revolutions per minute. For each case, the distance of the laser sheet from the fire deck was varied (z = 5, 10, and 20 mm) to investigate the axial variations in the flow field during the flow evolution in the compression stroke. A vortex identification algorithm was used to detect the swirl center and its deviation from the rigid body rotation. A Bessel fit was obtained using the experimental data. The result revealed that the in-cylinder flow was not axisymmetric. The swirl center approached the geometrical center as the piston approached the top dead center. The flow evolved at the farthest plane from the fire deck. The axial diffusion of angular momentum resulted in the formation of the swirl flow structure in the plane closer to the fire deck. Angular momentum analysis of a simplified geometry has been presented to explain the swirl amplification. The estimated results were compared with the experimental results to show the momentum stratification in the engine cylinder later in the compression stroke.

Heavy-Quark Momentum Broadening in a Non-Abelian Plasma away from Thermal Equilibrium.

We perform classical-statistical real-time lattice simulations to compute real-time spectral functions and momentum broadening of quarks in the presence of strongly populated non-Abelian gauge fields. Based on a novel methodology to extract the momentum broadening for relativistic quarks, we find that the momentum distribution of quarks exhibit interesting nonperturbative features as a function of time due to correlated momentum kicks it receives from the medium, eventually going over to a diffusive regime. We extract the momentum diffusion coefficient for a mass range describing charm and bottom quarks and find sizable discrepancies from the heavy-quark limit.

Flux‐gradient relations and their dependence on turbulence anisotropy

AbstractMonin–Obukhov similarity theory (MOST) is used in virtually all Earth System Models to parametrize the near‐surface turbulent exchanges and mean variable profiles. Despite its widespread use, there is high uncertainty in the literature about the appropriate parametrizations to use. In addition, MOST has limitations in very stable and unstable regimes, over heterogeneous terrain and complex orography, and has been found to represent the surface fluxes incorrectly. A new approach including turbulence anisotropy as a non‐dimensional scaling parameter has recently been developed and has been shown to overcome these limitations and generalize the flux‐variance relations to complex terrain. In this article, we analyze the flux‐gradient relations for five well‐known datasets, ranging from flat and homogeneous to slightly complex terrain. The scaling relations show substantial scatter and highlight the uncertainty in the choice of parametrization even over canonical conditions. We show that, by including information on turbulence anisotropy as an additional scaling parameter, the original scatter becomes well bounded and new formulations can be developed that drastically improve the accuracy of the flux‐gradient relations for wind shear () in unstable conditions and for temperature gradient () in both unstable and stable regimes. This analysis shows that both and are strongly dependent on turbulence anisotropy and allows us finally to settle the extensively discussed free convection regime for , which clearly exhibits a power law when anisotropy is accounted for. Furthermore, we show that the eddy diffusivities for momentum and heat and the turbulent Prandtl number are strongly dependent on anisotropy and that the latter goes to zero in the free convection limit. These results highlight the necessity to include anisotropy in the study of near‐surface atmospheric turbulence and lead the way for theoretically more robust simulations of the boundary layer over complex terrain.

Study of heat transfer in trihybrid nanofluid (Cu/Ag/Al2O3 with H2O) in Hele-Shaw cell and square enclosure with throughflow

The stability analysis of trihybrid nanofluid (Cu/Ag/ A l 2 O 3 as nanoparticles and H 2 O as base fluids) with spherical, brick, and cylindrical shapes, respectively, are examined theoretically and analytically with throughflow. Normal mode techniques have been used for linear stability analysis, and truncated Fourier series is carried out for nonlinear analysis. Comparison of Hele-Shaw cell and Square enclosure is performed in both linear and nonlinear analysis. Square enclosures are found to prevail in heat and mass transfer. Hele-Shaw number (HS number) has destabilizing behavior. Increase in concentration of nanoparticle increases the heat and mass transfer. Cylindrical shapes particles are found to have earlier rate of convection in both the system. Furthermore, throughflow exhibits destabilizing behavior. Hele-Shaw cell prevail heat and mass transfer on comparing for regular fluid. In all the three phases Prandtl number enhances the heat/mass transfer due to increase in momentum diffusivity of the fluid.

Statistical Properties of Exohiss Waves and Associated Scattering Losses of Radiation Belt Electrons

AbstractExohiss waves are a type of structureless whistler‐mode waves that exist in the low density plasmatrough outside the plasmapause and may potentially perturb the motions of electrons in the radiation belt and ring current. Using data from Van Allen Probe A, we analyze the distribution of magnetic power spectral density (PSD) of exohiss waves in different magnetic local time (MLT) and L‐shell regions near the geomagnetic equator. The results reveal that the peak magnetic PSD of exohiss waves is the weakest at MLT = 0–6 and the strongest at MLT = 12–18. The magnetic PSDs of exohiss waves are much lower than those of chorus and hiss waves except for the MLT = 12–18 sector. In addition, we calculated the quasi‐linear bounce‐averaged pitch angle and momentum diffusion coefficients (〈Dαα〉 and 〈Dpp〉) of electrons caused by exohiss waves. The diffusion coefficients are then compared with those caused by chorus and hiss waves. The peak 〈Dαα〉 of electrons driven by exohiss waves becomes stronger as L‐shell increases at all MLTs and is the greatest on the dayside, especially in the sector of MLT = 12–18. Exohiss waves have more significant effect on the loss of radiation belt electrons with specific energy levels related to MLT and L‐shell region compared to chorus and hiss waves. On the other hand, 〈Dpp〉 of electrons caused by exohiss waves is very small, which illustrates that exohiss waves have almost no acceleration effect on electrons.

Responses of quark-antiquark interactions and heavy quark dynamics to magnetic fields

We investigate the impact of the magnetic field generated by colliding nuclei on heavy quark-antiquark interactions and heavy quark dynamics in the quark-gluon plasma (QGP). By means of the hard-thermal-loop resummation technique combined with dimension-two gluon condensates, the static heavy quark potential and heavy quark momentum diffusion coefficient, which incorporate both perturbative and nonperturbative interactions between heavy quarks and the QGP medium, are computed beyond the lowest Landau level approximation. We find that the imaginary part of the heavy quark potential in the magnetic field exhibits significant anisotropy. Specifically, the absolute value of the imaginary part is larger when the quark-antiquark separation is aligned perpendicular to the magnetic field direction, compared to when it is aligned parallel to the magnetic field direction. The heavy quark momentum diffusion coefficient in the magnetized QGP medium also becomes anisotropic. As the temperature rises, the influence of higher Landau levels becomes increasingly significant, resulting in a decrease in the anisotropy ratio of the heavy quark momentum diffusion coefficient to values even below 1. At sufficiently high temperatures, this ratio ultimately approaches 1. The nonperturbative interactions are indispensable for understanding heavy quark dynamics in the low-temperature region. We also study the response of viscous quark matter to the magnetic field and explore its implications for heavy quark potential, thermal decay widths of quarkonium states, as well as heavy quark momentum diffusion coefficient. Published by the American Physical Society 2024

Intrinsic rotation modulation by diffusive neutral particles in tokamaks

The modulated transport model, a model kinetic ion transport equation for the pedestal and scrape-off layer (SOL), is generalized to self-consistently include effects of a single neutral particle species. The neutrals contribute additional transport terms, modifying the v∥ -dependent orbit-averaged ion diffusivities of the original work and the resulting predicted intrinsic rotation of the ions. After making simplifying assumptions of the neutral transport, in particular taking the continuous transport limit via a short charge-exchange step expansion, we derive relatively simple analytic expressions that capture the diffusive neutral physics. Within the scope of the model’s validity, the neutral-driven intrinsic rotation can compete with the turbulence-driven intrinsic rotation. However, for physically motivated parameters, the neutral-driven intrinsic rotation appears negligible, either on a term-by-term basis or due to a strong cancellation between the neutral-driven momentum diffusion and pinch terms. It appears that a treatment containing finite charge-exchange steps is necessary to capture neutral transport of strong flow momentum into the confined region from the SOL.

Subdiffusive processes in BWRs

The objective of this work is the analysis of subdiffusive processes in BWR reactors. Nuclear reactors are highly heterogeneous systems where the phenomena at the reactor scale are not possible to describe with constitutive standard laws (normal diffusion) of energy, momentum, and mass. However, there are methods to achieve it such as the volumetric average to upscale the reactor and incorporate up-scaled constitutive laws. However, it can also be proposed constitutive laws of fractional order to consider anomalous diffusion. For the neutronic processes, the neutron diffusion theory is non-appropriated to the reactor scale, because this theory is applied to the homogeneous reactor. Given the heterogeneity of these systems in describing the dynamic behaviour of BWRs with point models, it represents a challenge to the incorporation of the heterogeneous effects whose main characteristic is that the transport phenomena are subdiffusive with relaxation times (i.e., non-instantaneous) by nature. The point models called reducer-order models are important for stability analysis and to develop control strategies. In linear or nonlinear stability analysis and system control, they are carried out with reduced order models that are zero dimension, i.e., point models that depend exclusively on time. This is because existing methodologies propose mathematical expressions in the time or frequency domain for stability analysis or to establish control strategies. The challenge is for ROM models to be able to consider subdiffusive effects on neutron motion. This is achieved by various routes from the P1 theory that includes the temporal term with relaxation effects (relaxation time) or by proposing a more general constitutive equation of fractional order for the neutron current vector, as is presented in this work. Moreover, the Fractional Order Models behavior must be as a transport theory based model, as well as in those nuclear and thermohydraulic codes which are very useful but complex, for which is sometimes it is impossible to obtain analytical expressions. To incorporate these effects in this work we consider point models of fractional order, which represent the subdiffusive phenomenon when the fractional order (known as anomalous diffusion coefficient) is greater than 0 and less than 1.

Scalar QED Model for Polarizable Particles in Thermal Equilibrium or in Hyperbolic Motion in Vacuum

We consider a scalar QED (quantum electrodynamics) model for the frictional force and the momentum fluctuations of a polarizable particle in thermal equilibrium with radiation or in hyperbolic motion in a vacuum. In the former case the loss of particle kinetic energy due to the frictional force is compensated by the increase in kinetic energy associated with the momentum diffusion, resulting in the Planck distribution when it is assumed that the average kinetic energy satisfies the equipartition theorem. For hyperbolic motion in vacuum the frictional force and the momentum diffusion are similarly consistent with an equilibrium with a Planckian distribution at the temperature T=ℏa/2πkBc. The quantum fluctuations of the momentum imply that it is only the average acceleration a that is constant when the particle is subject to a constant applied force.