Time-dependent Velocity Research Articles

A note on thermal history kernel for unsteady heat transfer of a spherical particle

When a particle is subjected to an unsteady ambient flow, in terms of either time-dependent relative velocity or time-dependent temperature difference, the net heat transfer from the particle cannot be calculated based on the quasi-steady heat transfer correlation alone. Due to unsteady evolution of the thermal boundary layer, there is also a history contribution to heat transfer. The history contribution to heat transfer is expressed as a convolution integral of past evolution of temperature difference between the particle and the surrounding. While Basset history force and its finite Reynolds number extension have been well studied, similar understanding of unsteady heat transfer and thermal history kernel is lacking. We use existing particle-resolved simulation results to develop a finite Peclet number thermal history kernel, which when used with the convolution integral is demonstrated to accurately predict unsteady heat transfer over a range of Peclet numbers and particle-to-fluid heat capacity ratio.

Hydromagnetic Free Convective Flow of a Viscous Fluid With Constant Suction and Time Dependent Surface Velocity

Hydromagnetic Free Convective Flow of a Viscous Fluid With Constant Suction and Time Dependent Surface Velocity

Symmetric and Non-Symmetric Flows of Burgers’ Fluids through Porous Media between Parallel Plates

Unidirectional unsteady flows of the incompressible Burgers’ fluids between two infinite horizontal parallel plates are analytically studied when the magnetic and porous effects are taken into consideration. The fluid motion is induced by the two plates, which move in their planes with time-dependent velocities. Exact general expressions are established both for the dimensionless velocity and shear stress fields as well as the corresponding Darcy’s resistance in the channel using the Laplace transform. If both plates move with equal velocities in the same direction, the fluid motion becomes symmetric with respect to the mid-plane between them. Otherwise, its motion is non-symmetric. To bring to light the behavior of the fluid, the dimensionless velocity profiles versus the spatial variable as well as its time evolution are presented both for the symmetric and asymmetric case. Finally, for comparison, similar graphical representations are presented together for the velocities of the incompressible Oldroyd-B and Burgers’ fluids. For large values of the time t, as expected, the behavior of the two different fluids is almost identical. The Darcy’s resistance against y is also graphically represented for the symmetric flow at different values of the time t. The influence of the magnetic field on the fluid motion is graphically revealed and discussed.

One-dimensional dynamics of gaseous detonations revisited

Stability of one-dimensional gaseous detonations is revisited using both asymptotic analysis and high-order numerical simulations. The double limit of small heat release and a ratio of specific heats close to unity is considered, and attention is focused on weakly unstable detonations in the Chapman-Jouguet regime. It is shown that the time-dependent velocity of the lead shock can be obtained as the eigenfunction of a hyperbolic problem reducing to a single hyperbolic equation for the flow. The solution is then expressed in the form of an integral equation for the shock velocity, from which the threshold activation energy for transition to instability and the oscillation frequency can be obtained. These theoretical findings are validated against a set of direct numerical simulations of one-dimensional detonations in the same limit, performed using a high-order spectral difference scheme in which particular care is taken to ensure a high resolution of the flow with minimal numerical dissipation, while also suppressing post-shock numerical aberrations. Values of detonation parameters at the instability threshold obtained from numerical simulations are systematically compared against their theoretical counterparts, confirming the validity of the proposed asymptotic theory.

Accelerated magnetosonic lump wave solutions by orbiting charged space debris

The excitations of nonlinear magnetosonic lump waves induced by orbiting charged space debris particles in the Low Earth Orbital (LEO) plasma region are investigated in the presence of the ambient magnetic field. These nonlinear waves are found to be governed by the forced Kadomtsev–Petviashvili-type model equation, where the forcing term signifies the source current generated by different possible motions of charged space debris particles in the LEO plasma region. Different analytic lump wave solutions that are stable for both slow and fast magnetosonic waves in the presence of charged space debris objects are found for the first time. The dynamics of exact pinned accelerated magnetosonic lump waves is explored in detail. Approximate magnetosonic lump wave solutions with time-dependent amplitudes and velocities are analysed through perturbation methods for different types of localized space debris functions, yielding approximate pinned accelerated magnetosonic lump wave solutions. These new results may pave new directions in this field of research.

The influence of strain rate on the cavitation time and deformation of an underwater impulsively rectangular plate

The effect of strain rate on the cavitation time and elastoplastic deformation of steel rectangular plate subjected to underwater explosion load is analytically and numerically investigated in this study. At the cavitation time, the total pressure of the explosion is eliminated so that the cavitation time plays a significant role in the elastoplastic deformation of underwater explosive forming of plate. Taking into account the strain rate effect, the Cowper-Symond constitutive equation of mild steel is employed. Exact linear solution using the Eigen function and numerical linear and nonlinear solution using finite difference method (FDM) of dynamic response of impulsively plate is obtained. Implementing the linear work hardening, the stress, strain, displacement, and velocity in any steps of loading are calculated. The time of cavitation can be recognized in elastic or plastic regimes by applying the Cowper-Symond constitutive equation. Considering the strain rate influence, the effects of charge mass and standoff are investigated to occur of cavitation and time dependent deflection and velocity of a rectangular plate.

Acoustic time-dependent energy from force excited fluid loaded elastic shell/panel structures via a generalized modal radiation impulse response approach.

A generalized modal radiation impulse response approach is presented to evaluate the space-time surface velocity field, time-dependent force, instantaneous power, and energy transfer into a fluid resulting from the space-time force distribution of fluid loaded plate, shell, and panel structures. The basic approach utilizes the in vacuo eigenvectors of the structure to determine the in fluid response of the structure. Self-and mutual modal radiation impulse responses that couple the modal velocities of the fluid loaded structures are used to express the modal time-dependent velocities as a set of coupled convolution integral equations. A canonical fluid loaded single degree of freedom vibrator is addressed to illustrate the basic approach. A fluid loaded admittance impulse response is introduced and plays a central role in the analysis to evaluate the normal velocity resulting from a specified external force. A time-dependent energy equation is also introduced to investigate the temporal evolution of the internal energy loss and the energy transfer to the fluid. Numerical results are presented for an impulsive excitation of the fluid loaded single degree of freedom vibrator which serves as a canonical problem for investigating the response of complex structures.

Cell nucleus as a microrheological probe to study the rheology of the cytoskeleton

Mechanical properties of the cell are important biomarkers for probing its architectural changes caused by cellular processes and/or pathologies. The development of microfluidic technologies has enabled measuring the cell’s mechanical properties at high throughput so that mechanical phenotyping can be applied to large samples in reasonable timescales. These studies typically measure the stiffness of the cell as the only mechanical biomarker and do not disentangle the rheological contributions of different structural components of the cell, including the cell cortex, the interior cytoplasm and its immersed cytoskeletal structures, and the nucleus. Recent advancements in high-speed fluorescent imaging have enabled probing the deformations of the cell cortex while also tracking different intracellular components in rates applicable to microfluidic platforms. We present a, to our knowledge, novel method to decouple the mechanics of the cell cortex and the cytoplasm by analyzing the correlation between the cortical deformations that are induced by external microfluidic flows and the nucleus displacements, induced by those cortical deformations, i.e., we use the nucleus as a high-throughput microrheological probe to study the rheology of the cytoplasm, independent of the cell cortex mechanics. To demonstrate the applicability of this method, we consider a proof-of-concept model consisting of a rigid spherical nucleus centered in a spherical cell. We obtain analytical expressions for the time-dependent nucleus velocity as a function of the cell deformations when the interior cytoplasm is modeled as a viscous, viscoelastic, porous, and poroelastic material and demonstrate how the nucleus velocity can be used to characterize the linear rheology of the cytoplasm over a wide range of forces and timescales/frequencies.

Near-wall forces on a neutrally buoyant spherical particle in an axisymmetric stagnation-point flow

Abstract

The critical importance of mask seals on respirator performance: An analytical and simulation approach.

Filtering facepiece respirators (FFRs) and medical masks are widely used to reduce the inhalation exposure of airborne particulates and biohazardous aerosols. Their protective capacity largely depends on the fraction of these that are filtered from the incoming air volume. While the performance and physics of different filter materials have been the topic of intensive study, less well understood are the effects of mask sealing. To address this, we introduce an approach to calculate the influence of face-seal leakage on filtration ratio and fit factor based on an analytical model and a finite element method (FEM) model, both of which take into account time-dependent human respiration velocities. Using these, we calculate the filtration ratio and fit factor for a range of ventilation resistance values relevant to filter materials, 500-2500 Pa∙s∙m-1, where the filtration ratio and fit factor are calculated as a function of the mask gap dimensions, with good agreement between analytical and numerical models. The results show that the filtration ratio and fit factor are decrease markedly with even small increases in gap area. We also calculate particle filtration rates for N95 FFRs with various ventilation resistances and two commercial FFRs exemplars. Taken together, this work underscores the critical importance of forming a tight seal around the face as a factor in mask performance, where our straightforward analytical model can be readily applied to obtain estimates of mask performance.

Experimental quantification of oscillating flow in finite-length straight elastic vessels for Newtonian and non-Newtonian fluids

To better understand the complex flow in arteries it is necessary to analyze the fluid–structure interaction between the time dependent velocity field, the non-Newtonian fluid, and the elastic blood vessels and to investigate the wall-shear stress distribution that develops in the elastic vessel during an oscillation cycle. The scope of this study is to quantify the influence of the viscoelastic fluid properties on the fluid–structure interaction and the wall-shear stress of a straight elastic vessel by analyzing oscillatory flow of both a Newtonian reference fluid and a non-Newtonian fluid. Unlike in Womersley’s analyses, an elastic vessel of finite length with a non-Newtonian fluid is investigated in this study. Furthermore, quantitative benchmark data for numerical fluid–structure interaction methods are provided. Time-resolved particle-image velocimetry, static pressure measurements, and wall detection are used to measure the velocity field, the pressure distribution, and the vessel dilatation with high temporal and spatial resolution. The mechanical properties of the vessel material are determined by a dynamic mechanical analysis and the viscosities of the Newtonian and the non-Newtonian fluid are measured by a rheometer. The fluid–structure interaction is measured for a sinusoidal oscillating flow in a Reynolds number range 472≤ReNF≤971 and 503≤ReNNF≤1065 for the Newtonian reference fluid and the non-Newtonian fluid. The Womersley number range is 5.97≤WoNF≤8.53 for the Newtonian reference fluid and 6.14≤WoNNF≤8.79 for the non-Newtonian fluid. The results show that the wall-shear stress maximum increases up to 32%–38% for the non-Newtonian fluid despite a 10%–45% higher wall-shear rate for the Newtonian reference fluid. Furthermore, the amplitudes of the dilatation and the pressure in the vessel are more pronounced for the non-Newtonian fluid.

Cavitation phenomenon in penetration of rigid projectiles into elastic-plastic targets

This paper presents an analytical study on the cavitation phenomenon during penetration of a rigid projectile into an elastic-plastic target. The developed analytical approach is based on the general solution of the quasi-static and non-stationary dynamic cylindrical/spherical cavity expansion problem with assigned kinematic boundary condition at the cavity boundary (variable, time dependent radial velocity). An analytical projectile-target separation criterion is developed for a projectile having an arbitrary shape and for a target described by a simplified material model with a locked equation of state and a linear shear failure relationship. This relatively simple model may represent the behavior of different materials reasonably well yet allow an analytical solution of the problem. The paper derives the analytical expression of the contact zone size using both the cylindrical and spherical cavity expansion approaches and presents the related normal contact stresses acting on the projectile nose surface that maintains contact with the target. Examples of the developed formulation is presented for ogive nose and Rankine ovoid projectiles hitting aluminum targets, with a constant shear failure envelope, at different velocities and comparisons with known analytical and numerical solutions are shown. The effect of projectile and medium properties on the size of the contact zone are studied.

A Non-Iterative Integration Scheme Enriching the Solution to the Coupled Maglev Vehicle–Bridge System

A non-iterative integration scheme is presented in this study to enrich the solutions to the coupled equations of the maglev vehicle–bridge system. The proposed integration scheme is composed of two integration methods aiming at providing the solutions to equation of motion and state-space equation. First, the equation of motion of the simply supported girder bridge is transformed by the modal superposition method. Then the state-space equation is used to describe the motions of both the vehicle and the suspension control system, with the associated matrices assembled using the fully computerized approach. By adopting this integration scheme, only pure vector calculations arise in the solution process, regardless of the existence of time-dependent displacement and velocity on the right-hand sides of the two coupled equations. The proposed integration method is of the second-order accuracy with and without damping. Being equipped with adequate numerical dissipation and dispersion, the method also possesses the characteristic of little computing errors, as can be achieved through the use of different pairs of parameters. Finally, numerical simulations have been conducted to assess the influence of different feedback gains, three types of bridges with different lengths, and guideway irregularity on the maglev vehicle–bridge system.

The dynamics of parallel-plate and cone–plate flows

Rotational rheometers are the most commonly used devices to investigate the rheological behavior of liquids in shear flows. These devices are used to measure rheological properties of both Newtonian and non-Newtonian, or complex, fluids. Two of the most widely used geometries are flow between parallel plates and flow between a cone and a plate. A time-dependent rotation of the plate or cone is often used to study the time-dependent response of the fluid. In practice, the time dependence of the flow field is ignored, that is, a steady-state velocity field is assumed to exist throughout the measurement. In this study, we examine the dynamics of the velocity field for parallel-plate and cone–plate flows of Newtonian fluids by finding analytical solutions of the Navier–Stokes equation in the creeping flow limit. The time-dependent solution for parallel-plate flow is relatively simple as it requires the velocity to have a linear dependence on radial position. Interestingly, the time-dependent solution for cone–plate flow does not allow the velocity to have a linear dependence on radial position, which it must have at the steady state. Here, we examine the time-dependent velocity fields for these two flows, and we present results showing the time dependence of the torque exerted on both the stationary and rotating fixtures. We also examine the time dependence of spatial non-homogeneities of the strain rate. Finally, we speculate on the possible implications of our results in the context of shear banding, which is often observed in parallel-plate and cone–plate flows of complex fluids.

Observing traveling waves in glaciers with remote sensing: new flexible time series methods and application to Sermeq Kujalleq (Jakobshavn Isbræ), Greenland

Abstract. The recent influx of remote sensing data provides new opportunities for quantifying spatiotemporal variations in glacier surface velocity and elevation fields. Here, we introduce a flexible time series reconstruction and decomposition technique for forming continuous, time-dependent surface velocity and elevation fields from discontinuous data and partitioning these time series into short- and long-term variations. The time series reconstruction consists of a sparsity-regularized least-squares regression for modeling time series as a linear combination of generic basis functions of multiple temporal scales, allowing us to capture complex variations in the data using simple functions. We apply this method to the multitemporal evolution of Sermeq Kujalleq (Jakobshavn Isbræ), Greenland. Using 555 ice velocity maps generated by the Greenland Ice Mapping Project and covering the period 2009–2019, we show that the amplification in seasonal velocity variations in 2012–2016 was coincident with a longer-term speedup initiating in 2012. Similarly, the reduction in post-2017 seasonal velocity variations was coincident with a longer-term slowdown initiating around 2017. To understand how these perturbations propagate through the glacier, we introduce an approach for quantifying the spatially varying and frequency-dependent phase velocities and attenuation length scales of the resulting traveling waves. We hypothesize that these traveling waves are predominantly kinematic waves based on their long periods, coincident changes in surface velocity and elevation, and connection with variations in the terminus position. This ability to quantify wave propagation enables an entirely new framework for studying glacier dynamics using remote sensing data.

Hydromagnetic Free Convective Flow of a Viscous Fluid With Constant Suction and Time Dependent Surface Velocity

Hydromagnetic Free Convective Flow of a Viscous Fluid With Constant Suction and Time Dependent Surface Velocity

Heat Transfer Flow of Viscous Fluid with Constant Heat Source and Time Dependent Suction Velocity In Non-Homogeneous Porous Medium

Heat Transfer Flow of Viscous Fluid with Constant Heat Source and Time Dependent Suction Velocity In Non-Homogeneous Porous Medium

Numerical Calculations with a Multi-layer Model of Mixed Sand Transport Against Measurements in Wave Motion and Steady Flow

A multi-layer model is used to calculate time-dependent sediment velocity and concentration vertical profiles. This model, in which the differences in sediment transport at different distances from the bed are considered is intended both for the wave motion and steady flow. Numerical calculations were carried out for sediment transport during the wave crest and trough and total sediment transport as a sum of their absolute values. The model concept of variation in shear stress from the skin stress value above the bed to the stress value at the bed previously proposed for steady flow is extended here for the wave motion and verified by direct stress measurements. The calculations were carried out for mixed sand sediments with different grain size distributions including semi-uniform and poorly sorted grains. Comparison with the available small- and large -scale data from flumes and oscillating tunnels yields agreement typically within plus/minus a factor two of measurements.

Determination of Multileaf Collimator Positional Errors as a Function of Dose Rate, Speed, and Delivery Interruption for Volumetric-Modulated Arc Therapy Delivery.

Aim:To determine the multileaf collimator positional error (MLC-PE) during volumetric modulated arc therapy (VMAT) delivery by studying the time-dependent MLC velocity in mathematically derivable trajectories such as straight line and conic sections.Materials and Methods:VMAT delivery is planned in a way that MLCs are moving in a locus which can be defined by mathematical functions such as linear, parabolic, or circular velocity (PV or CV). The VMAT delivery was interrupted either once or multiple times during the delivery and projection images of the same were acquired in electronic portal imaging device. MLC-PE was then analyzed as a function of dose rate (DR), and MLC speed (SP) and number of interruptions in treatment delivery. In VMAT delivery with linear MLC motion, the delivery was interrupted either once (linear motion single interruption) or multiple (three) times (linear motion multiple interruptions). For PV and CV MLC velocity, the MLC motions are interrupted multiple times.Results:The maximum individual error obtained (DR of 35 MU/min, SP of 2.0 cm/s) was 1.96 ± 0.1 mm. Only 4.4% of MLCs showed ≥ ±1 mm positional error. When the treatment delivery is interrupted multiple times in VMAT delivery, the influence of interruption in MLC-PE overwhelmed the influence by DR and SP. For a sub-group analysis of independent and dependent variables, the mean MLC-PE was 0.18 ± 0.4 mm 0.19 ± 0.42 mm, respectively.Conclusion:Determination of MLC-PEs using a mathematical function without approximation indicates that MLC-PE is not a function of MLC speed. In less than 5% of the studied scenarios, the MLC-PE exceeds its tolerance value (±1 mm). The MLC-PE is significantly less in modern machines due to advancements in the delivery mechanism.

Fluid-Structure Interaction Simulation of Artificial Heart Valve Considering Open State of Cardiac Cycle

The dynamic finite element method with the fluid-structure interaction was used to investigate the deformation behavior of a newly developed artificial heart valve. To reproduce the opening movements of tri-leaflets of the valve during the half cardiac cycle, a time-dependent blood velocity was used as the boundary condition of the fluid domain. The nonslip boundary condition was also chosen for the tri-leaflets to ensure the viscous effect between the blood and the leaflet surfaces, while the free slip boundary condition was chosen for the cylindrical wall to ignore such viscous effect. The valve was assumed to be made from a natural tissue and a linear elastic material was assumed as the material model. The blood was assumed to be incompressible and Newtonian fluid. It was found that the valve was easily open when it came into contact with blood flow, taking only 0.3 seconds to go from fully closed to fully open. The blood flow was also found to be stable with a laminar state and free of turbulence.