Dimensionless Parameters Research Articles

Dynamic processes in current sheets and experimental laboratory astrophysics

The results of experimental research of the dynamics of current sheets, which are formed in laboratory experiments at the IOF RAS, are presented as a brief review. It is shown that the most significant features of phenomena like solar flares can be reproduced in laboratory conditions. These features include the relatively slow accumulation of the magnetic energy in the course of the current sheet formation, the rapid release of the energy during the disruption of the current sheet, acceleration of plasma flows, ultrafast plasma heating, and effective particle’s acceleration. A qualitative similarity has been established between the basic characteristics of current sheets in the tail region of the Earth’s magnetosphere and in laboratory conditions. A comparison of a number of fundamental dimensionless parameters indicates the possibility of quantitative laboratory modeling of processes occurring in the magnetosphere. It is concluded that experimental research of the dynamics of current sheets and magnetic reconnection processes represent one of the promising areas of the laboratory astrophysics.

MHD Al2O3/Cu-water Casson hybrid nanofluid flow across a porous exponentially stretching sheet

This study examines the heat and mass transmission of MHD Al2O3-Cu / H2O Casson hybrid- across an exponentially stretching porous sheet under the effect of non-uniform heat source/sink and chemical reaction. The nonlinear coupled ODEs are solved using the 3-stage Lobatto IIIa formula and the built-in MATLAB scheme Bvp4c after being converted from the governing nonlinear PDEs by appropriate similarity transformations. The numerical findings are compared with previously available works of literature in order to validate our investigations, and it transpires that there is a good agreement. Graphs are used to illustrate how dimensionless parameters such as the Casson parameter, magnetic parameter, radiation parameter, porosity parameter, Lewis number, the non-uniform heat source/sink parameter, and chemical parameter may affect a system. The impact of the Casson parameter on skin friction coefficient, Nusselt number, and Sherwood number are depicted in the table. The Casson hybrid nanofluid has been found out to have a greater thermal conductivity than the comparable Casson nanofluid. It was also found that the absolute value of the coefficient of skin friction & Nusselt number for Casson hybrid-nanofluid is increased by about 28% and 15% respectively when compared with Casson nanofluid.

The influence of a non-uniform heat source/sink and Joule heating on the convective motion of a micropolar fluid in a chemically radiative MHD medium across a stretched sheet

The objective of the present exploration is to examine impactions of radiation, a non-uniform intensity source, and a permeable medium on a temperamental MHD blended convective micropolar liquid over an extended sheet subject to Joule heating. To transform the formulated problem into ordinary differential equations, the applicable similarity transformation is implemented. By utilizing R-K-F 4th -5th order approach with shooting method with MATLAB, the numerical solution is obtained. For the relevant profiles, the dimensionless parameters are visually displayed and described. Skin friction, the Nusselt number, and the Sherwood number have all been calculated using the answer found for the velocity, temperature, and concentration. With the assistance of line graphs, the impact of different flow factors being introduced into the problem is addressed. This research is conducted on the implications of MHD, porous, thermal radiation, viscous dissipation, Joule heating, non-liner thermal radiation and chemical reaction. For large values of micropolar parameter, the temperature is reduced and velocity and angular momentum distributions are raised. With the thermal radiation parameter, the temperature distribution gets better and thermal boundary layer is improved while the large values of Eckert number and non-uniform heat source or sink parameters, thermal boundary layer is improved. The higher thermal conductivity is proportional to the thickness of the thermal boundary layer. The concentration profile degrades with higher Schmidt number and chemical reaction parameter values. The current examination pertains to the significant subject matter of cooling of systems, artificial heart identification, oil-pipelined frictions, flow-tracers.

Upscaling transport in heterogeneous media featuring local-scale dispersion: Flow channeling, macro-retardation and parameter prediction

Many theoretical treatments of transport in heterogeneous Darcy flows consider advection only. When local-scale dispersion is neglected, flux weighting persists over time; mean Lagrangian and Eulerian flow velocity distributions relate simply to each other and to the variance of the underlying hydraulic conductivity field. Local-scale dispersion complicates this relationship, potentially causing initially flux-weighted solute to experience lower-velocity regions as well as Taylor-type macrodispersion due to transverse solute movement between adjacent streamlines. To investigate the interplay of local-scale dispersion with conductivity log-variance, correlation length, and anisotropy, we perform a Monte Carlo study of flow and advective-dispersive transport in spatially-periodic 2D Darcy flows in large-scale, high-resolution multivariate Gaussian random conductivity fields. We observe flow channeling at all heterogeneity levels and quantify its extent. We find evidence for substantial effective retardation in the upscaled system, associated with increased flow channeling, and observe limited Taylor-type macrodispersion, which we physically explain. A quasi-constant Lagrangian velocity is achieved within a short distance of release, allowing usage of a simplified continuous-time random walk (CTRW) model we previously proposed in which the transition time distribution is understood as a temporal mapping of unit time in an equivalent system with no flow heterogeneity. The numerical data set is modeled with such a CTRW; we show how dimensionless parameters defining the CTRW transition time distribution are predicted by dimensionless heterogeneity statistics and provide empirical equations for this purpose.

Experimental Study on Pressure Oscillation Characteristics of Di-N-Butyl Ether in a Constant Volume Vessel

ABSTRACT This paper conducted experimental research on spontaneous pressure oscillation characteristics of di-n-butyl ether (DBE). Based on a constant volume vessel (CVV) with 210 mm in length and 180 mm in diameter, the initial pressure, temperature, and equivalence ratio ranges of 0.05–0.3 MPa, 373–453 K, and 0.7–1.6. The experimental data of combustion pressure, CVV vibration and sound pressure were analyzed. The results indicate that DBE exhibits the strongest pressure oscillation at high pressures, moderate temperatures and equivalence ratios. The highest oscillation intensity is achieved at 0.3 MPa, 433 K, equivalence ratio of 1.4. The vibration and sound pressure signals exhibit the same patterns as combustion pressure signals. Spectrum analysis is conducted by Fast Fourier Transform of pressure signals, it shows that the amplitude of the characteristic frequency increases with the increase of oscillation intensity. In addition, to further reveal the influence of combustion instability on oscillation intensity, the dimensionless parameter Peclet number and critical radius are compared, it shows that the combustion instability has strong effect on pressure oscillation, and diffusive-thermal instability is the key factor that influences pressure oscillation. This study is believed to be beneficial for organizing better combustion for internal combustion engines.

Experiment and restoring force model study of precast shear walls with new rabbet-unbonded horizontal connection

The 'rabbet-unbonded horizontal connection' (RUHC) is a new connection form of precast shear wall. This study conducted a low-cycle repeated loading test on three RUHC walls to investigate the hysteretic performance of the walls with the 'axial compression ratio' and 'unbonded level' as the main variables and the results showed that the above two parameters remarkably affected the seismic performance of RUHC walls. Based on the analysis of test skeleton and hysteresis curve characteristic, the influence of parameters such as axial compression ratio and unbonded level on the load and displacement during the loading process was analyzed. The theoretical values of yield, peak and limit points were calculated, and the skeleton curve model was proposed. Moreover, the unloading stiffness formula was proposed by the non-linear relation of dimensionless parameters and Matlab software fitting, and the hysteresis rule model was established. Finally, a three-fold-linear restoring force model of RUHC walls composed of the theoretical skeleton curve and hysteresis rule was established and verified. This model provides an effective prediction for the hysteresis characteristics and a theoretical basis for conducting elastic-plastic analysis of RUHC structures.

An easy-to-use analytical model for standing column wells operating with bleed

Accurate assessment of subsurface heat transport is vital for the design of standing column well systems. When bleed is utilized, the mathematical problem is governed by coupled heat transfer and groundwater flow within a radially convergent flow field, making the development of models challenging. While numerical models exist to simulate these transient processes, the absence of simple and accessible analytical solutions limits their broader application. This study addresses this gap by developing a novel easy-to-use analytical model to accurately represent the heat advection–diffusion problem in standing column wells operating with bleed. The proposed model combines the well-known infinite line source model with an innovative scaling function, inspired from the field of solute transport, through a simple convolution product. Notably, the developed model depends on only three dimensionless parameters: dimensionless advection time, Péclet number, and bleed ratio. Rigorous validation against two distinct sets of reference numerical solutions demonstrated the model’s efficiency, accuracy, and reliability across a broad spectrum of nine physical parameters. Key results include relative root mean square errors on the order of 10−3 across 200 reference solutions, confirming the model’s robustness. These findings highlight the model’s potential to significantly advance both research and practical applications in the design and optimization of standing column wells.

Microscopic analysis of relaxation behavior in nonlinear optical conductivity of graphene

We produce a general formalism to study the interband dynamical optical conductivity in the nonlinear regime of graphene in the presence of a quantum bath comprising phonons and electrons. When a quantum solid of graphene is subjected to an intense electric field in the optical frequency range, the observation of a nonlinear response is facilitated by formulating a quantum master equation of the density operator associated with the Hamiltonian encapsulated in a spin-boson model of dissipative quantum statistical mechanics. Our results reveal the nonlinear steady-state regime’s population inversion and decoherence. The present method enables us to investigate further the nonlinear interband optical conductivity of pristine and gapped graphene characterized by a single dimensionless parameter at finite temperatures. Different bath spectra’ effects on phonons and electrons are examined in detail. The temperature dependence of conductivity reveals that changing temperature can enable us to make a transition from the linear to the nonlinear regime for fixed optical field parameters. Interestingly, a fascinating switching-like behavior is observed for the low-temperature optical conductivity of the gapped graphene while we vary the energy gap as well as the frequency of the externally applied field. Although our general formulation can address a variety of nonequilibrium responses of the two-band system, it also facilitates a connection with the phenomenological modeling of nonlinear optical conductivity.

Flow Evolution and Vertical Accelerations in Wave‐Swash Interactions

AbstractWe report on a laboratory study of wave‐swash interactions, which occur in the very nearshore environment of a beach when the shallow swash flow of a breaking wave interacts with a subsequent wave. Wave‐swash interactions have been observed in the field, hypothesized to be important for nearshore transport processes, and categorized into different qualitative types, but quantitative descriptions of their dynamics have remained elusive. Using consecutive solitary waves with different wave heights and separations, we generate a wide variety of wave‐swash interactions with large flow velocities and vertical accelerations. We find that wave‐swash interactions can be quantitatively characterized in terms of two dimensionless parameters. The first of them corresponds to the wave height ratio for consecutive waves, and the second is a dimensionless measure of the time separation between consecutive wave crests. Using measurements of bed pressure and free‐surface displacement, we estimate the total vertical accelerations and focus on the peak upward‐directed acceleration. We find that wave‐swash interactions can generate vertical accelerations that can easily exceed gravity, despite occurring in very shallow water depths. The large vertical accelerations are upward‐directed and are quickly followed by onshore‐directed horizontal velocities. Together, our findings suggest that wave‐swash interactions are capable of inducing large material suspension events of sediment or solutes in sediment pores, and transporting them onshore. While the data are from a single location making it difficult to generalize the findings across the swash zone, the results clearly demonstrate the importance of large vertical accelerations in wave‐swash interactions.

Oscillatory excitation of Faraday waves on the interface of immiscible fluids in a slotted channel

Recent studies of the oscillatory dynamics of the interface between fluids in Hele–Shaw cells have revealed a new type of instability termed the “oscillatory Saffman instability” in the case of fluids with high-viscosity contrast. The present study is dedicated to the experimental investigation of the dynamics of the interface between low-viscosity fluids of different densities oscillating in a vertical narrow channel. It is discovered that as the amplitude of oscillations increases, a threshold excitation of parametric oscillations of the interface in the form of a standing wave is observed in the plane of the fluid layer. This phenomenon bears a resemblance to Faraday waves, but the dependence of the standing wave wavelength on the oscillation frequency does not align with the classical dispersion relation for low-viscosity fluids. The damping effect of viscous boundary layers near the cell walls and the out-of-plane curvature of the oscillating interface leads to a decrease in the natural frequency of oscillations. The experiments demonstrate a significant role of the dimensionless layer thickness. With its decrease (increase in the dimensionless out-of-plane interface curvature), the threshold oscillation acceleration rises in accordance with a power law. To the best of the authors' knowledge, this type of instability has been discovered and studied for the first time. Another important finding is the excitation of intense time-averaged vortical flows in the channel plane within the supercritical region. The physical mechanism underlying the excitation of the time-averaged vortices is clarified, and the dimensionless parameters that govern their intensity are identified.

Detecting Instantaneous Tidal Signals in Ocean Models Utilizing Streaming Band‐Pass Filters

AbstractThrough the implementation of a streaming filter, output of numerical ocean simulations can be band‐pass filtered at tidal frequencies while the model is running, yielding time series of sinusoidal motions consisting of tidal signals in the filter's target frequency band. The filtering algorithm is developed from a system of two ordinary differential equations that represents the motion of a damped harmonic oscillator. The filter's response to a broadband input signal is unity at its target frequency but vanishes toward the low and high frequency limits. The decay of the filter response is controlled by a dimensionless parameter, which determines the filter's bandwidth. As a result, the filter allows signals within a small frequency band around its target frequency to pass through, while blocking signals outside of its target frequency band. In this work, the filtering algorithm is implemented into the barotropic solver of the Modular Ocean Model version 6 (MOM6) for determining the instantaneous tidal velocities of the semi‐diurnal and diurnal tides. Utilizing the filters, the frequency‐dependent internal wave drag is applied to the semi‐diurnal and diurnal frequency bands separately. The simulation results suggest that the performance of the algorithm is consistent with the filter transfer function in Fourier space. Potential applications of the algorithm also include de‐tiding the model output for nested regional ocean models, especially those for the purpose of operational forecasting.

Study of relativistic hot accretion flow around Kerr-like wormhole

We investigate the structure of relativistic, low-angular momentum, inviscid advective accretion flow in a stationary axisymmetric Kerr-like wormhole (WH) spacetime, characterized by the spin parameter (a k), the dimensionless parameter (β), and the source mass (M WH). In doing so, we self-consistently solve the set of governing equations describing the relativistic accretion flow around a Kerr-like WH in the steady state, and for the first time, we obtain all possible classes of global accretion solutions for transonic as well as subsonic flows. We study the properties of dynamical and thermodynamical flow variables and examine how the nature of the accretion solutions alters due to the change of the model parameters, namely energy (ℰ), angular momentum (λ), a k, and β. Further, we separate the parameter space in λ-ℰ plane according to the nature of the flow solutions, and study the modification of the parameter space by varying a k and β. Moreover, we retrace the parameter space in a k-β plane that allows accretion solutions containing multiple critical points. Finally, we calculate the disc luminosity (L) considering free-free emissions for transonic solutions as these solutions are astrophysically relevant and discuss the implication of this model formalism in the context of astrophysical applications.

Stochastic excitation of waves in magnetic stars

Context. Stellar oscillations are key to unravelling stellar properties, such as their mass, radius, and age. This in turn enables us to date and characterize their exoplanetary systems. The amplitudes of acoustic (p-) modes in solar-like stars are intrinsically linked to their convective turbulent excitation source, which in turn is influenced by magnetism. In the observations of the Sun and stars, the mode amplitudes are modulated following their magnetic activity cycles: the higher the magnetic field, the lower the mode amplitudes. When the magnetic field is strong, it can even inhibit acoustic modes, which are not detected in most of the solar-like stars that are strongly magnetically active. Magnetic fields are known to freeze convection when they stronger than a critical value: the so-called on-off approach is used in the literature. Aims. We investigate the impact of magnetic fields on the stochastic excitation of acoustic modes. Methods. First, we generalise the forced-wave equation formalism, including the effects of magnetic fields. Second, we assess how convection is affected by magnetic fields using results from the magnetic mixing-length theory. Results. We provide the source terms of the stochastic excitation, including a new magnetic source term and the Reynolds stresses. We derive scaling laws for the mode amplitudes that take both the driving and the damping into account. These scalings are based on the inverse Alfvén dimensionless parameter: The damping increases with the magnetic field and reaches a saturation threshold when the magnetic field is strong. The driving of the modes diminishes when the magnetic field becomes stronger and the turbulent convection is weaker. Conculsions. As expected from the observations, we find that a stronger magnetic field diminishes the resulting mode amplitudes. The evaluation of the inverse Alfvén number in stellar models provides a means for estimating the expected amplitudes of acoustic modes in magnetically active solar-type stars.

Inertia effect of deformation in amorphous solids: A dynamic mesoscale model

Shear transformation (ST), as the fundamental event of plastic deformation of amorphous solids, is commonly considered as transient in time and thus assumed to be an equilibrium process without inertia. Such an approximation however poses a major challenge when the deformation becomes non-equilibrium, e.g., under the dynamic and even shock loadings. To overcome the challenge, this paper proposes a dynamic mesoscale model for amorphous solids that connects microscopically inertial STs with macroscopically elastoplastic deformation. By defining two dimensionless parameters: strain increment and intrinsic Deborah number, the model predicts a phase diagram for describing the inertia effect on deformation of amorphous solids. It is found that with increasing strain rate or decreasing ST activation time, the significant inertia effect facilitates the activation and interaction of STs, resulting in the earlier yield of plasticity and lower steady-state flow stress. We also observe that the externally-applied shock wave can directly drive the activation of STs far below the global yield and then propagation along the wave-front. These behaviors are very different from shear banding in the quasi-static treatment without considering the inertia effect of STs. The present study highlights the non-equilibrium nature of plastic events, and increases the understanding of dynamic or shock deformation of amorphous solids at mesoscale.

Gravitational collapse at low to moderate Mach numbers: The relationship between star formation efficiency and the fraction of mass in the massive object

The formation of massive objects via gravitational collapse is relevant both for explaining the origin of the first supermassive black holes and in the context of massive star formation. Here, we analyze simulations of the formation of massive objects pursued by different groups and in various environments, concerning the formation of supermassive black holes, primordial stars, as well as present-day massive stars. We focus here particularly on the regime of small virial parameters, that is, low ratios of the initial kinetic to gravitational energy, low to moderate Mach numbers, and the phase before feedback is very efficient. We compare the outcomes of collapse under different conditions using dimensionless parameters, particularly the star formation efficiency є*, the fraction ƒ* of mass in the most massive object relative to the total stellar mass, and the fraction ƒtot of mass of the most massive object as a function of the total mass. We find that in all simulations analyzed here, ƒtot increases as a function of є*, although the steepness of the increase depends on the environment. The relation between ƒ* and є* is found to be more complex and also strongly depends on the number of protostars present at the beginning of the simulations. We show that a collision parameter, estimated as the ratio of the system size divided by the typical collision length, allows us to approximately characterize whether collisions are important. A high collision parameter implies a steeper increase in the relation between ƒtot and є*. We analyze the statistical correlation between the dimensionless quantities using the Spearman coefficient and further confirm via a machine learning analysis that good predictions of ƒ* can be obtained from є* together with a rough estimate of the collision parameter. This suggests that a good estimate of the mass of the most massive object can be obtained once the maximum efficiency for a given environment is known and an estimate for the collision parameter has been determined.

On the mechanics of conducting micropolar fluids with magnetic particles: Vorticity–microrotation difference

In this paper, mechanisms that differentiate microrotation (i.e., particles' internal rotation) and vorticity in magnetohydrodynamic micropolar flows with magnetic particles are examined. Micropolar fluids are characterized by the asynchronization of the microrotation and the vorticity of the liquid carrier. When the microrotation is equal to the fluid's vorticity, the flow is purely Newtonian. In this context, two classical examples of micropolar magnetohydrodynamic fluids with magnetic particles are used, namely, blood and ferrofluid. The effect of all dimensionless parameters associated with the mathematical model is examined in terms of differentiating microrotation and vorticity. These dimensionless parameters are specifically calculated using the physical properties of the ferrofluid and blood. It was shown that higher values of the rotational viscosity (which are associated with smaller values of the spin relaxation time), higher values of channel's height, and higher values of the microrotation wall parameter tend to equalize microrotation and vorticity. On the other hand, the spin viscosity and the micromagnetorotation (magnetic torque) are mechanisms that differentiate microrotation and vorticity. Lorentz force does not seem to have any noticeable effect on the microrotation–vorticity difference. It is anticipated that this study will reveal the cases where a magnetohydrodynamic micropolar fluid with magnetic particles, such as blood and ferrofluid, can be simplified to a Newtonian one, which brings many benefits associated with a simplified mathematical flow model (such as smaller computational cost and less time).

Theory of similarity and ultrasonic testing

Application of similarity theory (dimensional analysis) to ultrasonic (UT) testing is discussed using as an illustration the example of concrete blocks. The concept of dimensional analysis makes it possible to represent a physical system via a minimal set of variables, the so-called π groups, which are the dimensionless quantities. These dimensionless parameters, characterizing the respective phenomenon, should have approximately equal values for the real object and for the model. Small concrete samples have been tested in the lab conditions using various UT probes and techniques. Two dimensionless criteria, valid and similar for the real field case and for the laboratory samples, have been introduced: total attenuations of UT waves and ratios of void size to the UT wavelength. To get total attenuations in the field conditions for thick concrete block, similar to the total attenuations measured in lab experiments on small samples, one should apply the low-frequency UT waves 60-100kHz. However, these UT waves will be able to reliably detect only the large inhomogeneities (e.g. voids), whose size is about half of the used UT wave, i.e. inhomogeneities with dimensions larger than 20-40mm.

Dynamics of non-Newtonian droplets eccentrically impacting hydrophobic spherical surfaces

In this study, the dynamic behaviors of non-Newtonian fluid droplets with shear-thinning properties eccentrically impacting hydrophobic particle surfaces are investigated through a combination of numerical simulations and experiments. The simulation integrates the dynamic contact angle and a non-Newtonian fluid power-law model within the volume of fluid model framework. The effects of apparent viscosity (η), impact velocity (v0), and dimensionless eccentricity parameter (B) on the dynamic behaviors of non-Newtonian droplets are analyzed. Furthermore, the study offers insight into the progression of pressure distribution, kinetic energy, and liquid viscosity across droplets during the entire impact process. An energy balance analysis, which includes kinetic energy, surface energy, potential energy, and viscous dissipation, is employed to elucidate the fundamental physical mechanisms that govern the dynamics of eccentric impacts of non-Newtonian droplets. Finally, a model (Recr D* = −95.7 + 11 450.6e−B/0.18) is proposed to predict the adhesion or detachment of shear-thinning droplets eccentrically impacting hydrophobic particle surfaces.

Annular Newtonian Poiseuille flow with pressure-dependent wall slip

We investigate the effect of pressure-dependent wall slip on the steady Newtonian annular Poiseuille flow employing Navier’s slip law with a slip parameter that varies exponentially with pressure. The dimensionless governing equations and accompanying auxiliary conditions are solved analytically up to second order by implementing a regular perturbation scheme in terms of the small dimensionless pressure-dependence slip parameter. An explicit formula for the average pressure drop, required to maintain a constant volumetric flowrate, is also derived. This is suitably post-processed by applying a convergence acceleration technique to increase the accuracy of the original perturbation series. The effects of pressure-dependent wall slip are more pronounced when wall slip is weak. However, as the slip coefficient increases, these effects are moderated and eventually eliminated as the perfect slip case is approached. The results show that the average pressure drop remains practically constant until the Reynolds number becomes sufficiently large. It is worth noting that all phenomena associated with pressure-dependent wall slip are amplified as the annular gap is reduced.

Acoustics of wet porous media with evaporation/condensation

This paper investigates acoustic wave propagation in wet rigid-frame porous media accounting for evaporation and condensation. At equilibrium, the solid walls are covered by a thin water film, and water vapor in the air is at its temperature-dependent saturation pressure. Small acoustic perturbations cause water to vaporize or condense, which together with the reversibility of the phase change, lead to a linear problem where the usual local poro-acoustics physics is enriched with the (i) Clapeyron relation linking liquid-wall temperature, vapor pressure, and latent heat of vaporization, (ii) latent heat transfer in the solid frame, (iii) diffusion equation for water vapor in air, and (iv) water vapor's equation of state. The equilibrium temperature highly influences the vapor concentration and the physical parameters of saturated moist air. Using the two-scale asymptotic homogenization method, it is shown that the dynamic permeability is determined similarly to classical porous media, while the effective compressibility is modified by evaporation/condensation and the equilibrium temperature. This modification is influenced by vapor mass and heat flows associated with phase changes through a local fully coupled heat transfer and water vapor diffusion problem, with specific boundary conditions at the gas–water interface. The analysis identifies dimensionless parameters and characteristic frequencies defining the upscaled model's features. Depending on equilibrium temperature, the theory qualitatively and quantitatively determines the characteristics of acoustic waves propagating through the media. The results are illustrated and discussed with analytically developed models.