Viscous Energy Dissipation Research Articles

Dynamic and kinematic characteristics of unsteady motion of a water-in-oil emulsion droplet in collision with a solid heated wall under conditions of convective heat transfer

The paper presents the experimental results of spreading, fingering and corona-like splashing of water-in-oil emulsion droplets based on n-decane, isoparaffin oil and distilled water in the range of Weber numbers We = 100–900, wall temperatures Tw = 20–80 °C and in collision with a smooth solid surface. The spreading features and separate convective rolling structures in emulsion droplets are examined at the late stages of wetting. The effect of Tw on the viscous dissipation energy and the maximum spreading coefficient is established. The validity of the assumptions explaining the contradictory behavior of the maximum spreading diameter of emulsion droplets with increasing temperature is studied. The assumption of unstable behavior of the emulsion droplet rim during spreading is proposed. The maximum emulsion corona diameter and height decrease linearly with the Tw growth due to the longer corona lifetime. The maximum corona diameter increases following the power law with increasing the Brinkman number due to an increase in the liquid viscosity and a decrease in Tw. The results help to predict the corona's behavior by determining the relationship between the viscous dissipation of the spreading liquid and the energy transferred to the liquid from the wall due to molecular (thermal) conduction.

Comparative Study on the Spreading Behavior of Oil Droplets over Teflon Substrates in Different Media Environments.

This paper comparatively investigated the spreading process of an oil droplet on the surface of highly hydrophobic solid (Teflon) in air and water media using a high-speed imaging technology, and analyzed their differences in spreading behavior from the perspective of empirical relations and energy conservation. Furthermore, the classical HD and MKT wetting models were applied to describe the oil droplet spreading dynamics to reveal the spreading mechanism of oil droplets on the Teflon in different media environments. Results showed that the entire spreading process of oil droplets on Teflon in air could be separated into three stages: the early linear fast spreading stage following , the intermediate exponential slow spreading stage obeying , and the late spreading stage described by . However, the dynamics behavior of dynamic contact angle during the oil droplet spreading on Teflon in water could be well described by these expressions, and . Clearly, a significant difference in the oil droplet spreading behavior in air and water media was found, and the absence of the intermediate exponential spreading stage in the oil–water–Teflon system could be attributed to the difference in the dissipated energy of the system because the dissipation energy in the oil–water–solid system included not only the viscous dissipation energy of the boundary layer of oil droplet, but also that of the surrounding water which was not included in the dissipation energy of the oil–air–solid system. Moreover, the quantitative analysis of wetting models suggested that the MKT model could reasonably describe the late spreading dynamics of oil droplets (low TPCL velocities), while the HD model may be more suitable for describing the oil droplet spreading dynamics at the early and intermediate spreading stages (high TPCL velocities).

On the Prandtl-Kolmogorov 1-equation model of turbulence.

We prove an estimate of total (viscous plus modelled turbulent) energy dissipation in general eddy viscosity models for shear flows. The ratio of the near wall average viscosity to the effective global viscosity is the key parameter in the estimate. This result is then applied to the 1-equation, URANS model of turbulence for which this ratio depends on the specification of the turbulence length scale. The model, which was derived by Prandtl in 1945, is a component of a 2-equation model derived by Kolmogorov in 1942 and is the core of many unsteady, Reynolds averaged models for prediction of turbulent flows. Let τ denote a selected time scale. Away from walls, interpreting an early suggestion of Prandtl, we set [Formula: see text]In the near-wall region analysis suggests replacing the traditional [Formula: see text] ([Formula: see text] wall normal distance) with [Formula: see text] giving [Formula: see text]This specification of [Formula: see text] results in a simpler model with correct near wall asymptotics. Its energy dissipation rate scales no larger than the physically correct [Formula: see text], balancing energy input with energy dissipation. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 2)'.

On the maximal spreading of drops impacting onto a no-slip substrate

We numerically study the impact of a liquid drop onto no-slip rigid substrates with different wettabilities using a diffuse interface method, aiming to obtain a universal model for the maximal spreading of the impacting drop at moderate Weber numbers. We find that the wettability plays an important role in the maximal spreading and that the ratio of the surface energy to the initial kinetic energy of the drop at the maximal spreading, η, follows η∼We−1/2 at high fixed Reynolds numbers, where We is the Weber number. Taking account of the wettability effect, we obtain a scaling law at high Reynolds numbers from an analysis of energy transformation. This scaling law is compatible with the one derived from the momentum balance at the high impact velocity by Clanet et al. [“Maximal deformation of an impacting drop,” J. Fluid Mech. 517, 199–208 (2004)]. Moreover, we attribute it to the presence of a viscous–capillary regime, in which the viscous dissipation of the kinetic energy from the substrate is as significant as the kinetic energy transformed into the surface energy. Accordingly, we identify a new impact parameter, which makes all the numerical results of maximum drop deformation (from the viscous regime to the viscous–capillary regime with Reynolds number up to 104) collapse onto a single curve. Finally, we propose a universal model, the predictions of which are shown to agree well with numerical results for a wide range of Weber and Reynolds numbers.

The poroviscoelastodynamic solution to Mandel's problem

Mandel's problem of quasi-static poroelasticity describes axial compression of a rectangular sample from a porous, fluid-saturated, and elastic material while allowing the pore fluid to drain from the lateral boundaries. This paper reports the closed-form analytical solution to an extension of this problem that considers dynamic response of a porous, fluid-saturated, and viscoelastic specimen with similar geometry and boundary conditions to harmonic excitation. Biot's theory of poroelastodynamics, along with frequency-domain formulation of the viscoelastic constitutive behavior, are used for this purpose. Results indicate that a quasi-static approximation of the dynamic Mandel's problem could generate significantly deviant results compared to the presented dynamic solution, even at frequencies that are substantially smaller than the first natural frequency of the specimen. In this aspect, the solution delineates the existence of four timescale categories pertaining to viscous energy dissipation within the solid and fluid phases of the tested material, as well as the specimen natural frequencies and the loading excitation frequency. Relative order of the described timescales is shown to shape the various forms that the sample frequency response may take. These variations are demonstrated via three case studies involving the brain tissue, asphalt mix, and shale. The presented poroviscoelastodynamic solution verifies previous findings from experimental studies suggesting that a disentangled exhibition of the poroelastic and viscoelastic energy dissipation mechanisms may be captured by the loss angle curves of a frequency sweep test on poroviscoelastic materials.

Inertial energy dissipation in nuclear dynamics

We present the TDDFT+Langevin model that incorporates microscopic time-dependent density function theory (TDDFT) with macroscopic Langevin model. By extracting the energy-dependent dissipation effect from the TDDFT dynamics, quantum effects are introduced to the Langevin-type stochastic fission analysis. In this paper, by means of Skyrme nuclear effective interactions, the energy-dependent friction coefficients to be used in Langevin calculations are provided individually for 25 fission nuclei chosen from uranium, plutonium, curium, californium, and fermium isotopes. The validity of the energy-dependent friction coefficients are confirmed by comparing to the existing experimental fission fragment yields. In conclusion, depending on the energy, the transition of energy dissipation mechanism from conventional viscous energy dissipation to inertial energy dissipation is shown.

A geometrical criterion for the dynamic snap-off event of a non-wetting droplet in a rectangular pore–throat microchannel

In porous media, non-wetting phase droplets snapping off in a constricted microchannel are one of the most common phenomena in two-phase flow processes. In this paper, the application range of the classic quasi-static criterion in rectangular cross section microchannels is obtained. For three different droplet breakup phenomena—total breakup, partial breakup, and non-breakup—observed in experiments when a non-wetting phase droplet passes through a microchannel constriction, the breakup is caused by the droplet neck snapping off in a channel constriction. A critical criterion for the dynamic snap-off event in a two-phase flow is proposed considering the effect of viscous dissipation by mechanical analysis, energy dissipation analysis, and many microfluidic experiments. When the droplet front flows out of the constriction, snap-off will occur if the surface energy release exceeds the required energy for viscous dissipation and kinetic energy conversion. The unique partial breakup phenomenon is affected by droplet surfactant distribution and the acceleration effect in the constriction center. This partial breakup phenomenon in experiments is an essential evidence for the non-uniform distribution of surfactants in the droplet surface. The results of this study contribute to understanding pore-scale mass transfer and flow pattern changes within porous media.

Severe MAC increases shear stresses on particles traversing the mitral valve: an in vitro study

Abstract Funding Acknowledgements Type of funding sources: None. Background Mitral annular calcification (MAC) is a strong predictor of stroke but mechanism(s) are poorly defined. Severe MAC can produce a gradient across the mitral valve (MV) and, when studied in vitro, disturbs normal flow across the valve resulting in increased viscous energy dissipation. Purpose We hypothesized that severe MAC would increase shear stress on particles traveling across the MV into the left ventricle (LV). Given that shear stresses cause platelet activation this might represent a mechanism by which MAC could increase stroke risk. Methods A silicone model MV was created using a 3D TEE dataset. 3D printed calcium phantoms were incorporated into the valve simulate severe MAC. The valve was tested in a left heart duplicator under rest and exercise conditions and compared with a duplicate valve without the calcium phantoms. Fine particles suspended in a water/glycerol blood analogue allowed for measurement of vortex formation and shear stresses using particle image velocimetry (PIV). Particle residence time (PRT) maps were created to assess how long blood particles would remain in the LV. Particle residence index (PRI - ratio of remaining particles in LV/initial number of particles) is a more quantitative measure of how fast particles leave the LV. These calculations were used to approximate viscous shear stresses on blood particles. For each particle the induced viscous shear stress was evaluated for the entire duration of residence in the LV. Results For the normal MV all released particles left the LV by the 3rd cycle; with severe MAC particles completely left the LV shortly after the 7th cycle. PRI measurements confirmed that particles remained longer in the LV in the presence of severe MAC (figure 1). MAC also induced a shift in the accumulated shear stress levels from the high range > 0.4 Pa.s and the low range < 0.1 towards the middle region (0.16-0.32 Pa.s, figure 2). As shear stress is reported for one cycle, one may expect MAC to lead to higher accumulated higher viscous stresses as particles reside in the LV for a longer time. Conclusions In the presence of severe MAC blood particles remain longer in the LV and are exposed to greater cumulative shear stresses vs the normal situation. Given that shear stress is known to cause platelet activation this may be a mechanism by which MAC increases risk of ischemic stroke. Abstract Figure 1 Abstract Figure 2

Viscous energy dissipation of kink waves due to phase mixing in twisted coronal flux tubes

ABSTRACT We have studied viscous energy damping of kink Magnetohydrodynamic (MHD) waves in weakly twisted magnetic flux tubes. The flux tube has been modelled as a homogeneous internal region with a straight magnetic field, surrounded by a radially non-uniform and magnetically twisted transitional layer embedded in a homogeneous ambient with a straight field. Using a modal expansion technique, we have solved an initial value problem for the incompressible viscous MHD equations and obtained spatio-temporal behaviour of the perturbations of the kink mode in linear regime. In the transitional layer, the perturbations are subject to phase mixing which enhances the viscous effects in the region. We show that magnetic twist can increase or decrease the efficiency of viscous damping of the phase-mixed perturbations in the non-uniform transitional layer. Using the temporal evolution of the total energy, we have obtained the viscous dissipation time as a power function of the Reynolds number. Our results show that magnetic twist could decrease or increase the viscous dissipation time.

Application of Arrhenius chemical process on unsteady mixed bio-convective flows of third-grade fluids having temperature-dependent in thermo-rheological properties

This article presents the unsteady mixed convective flow of third-grade fluid flow comprising nanoparticles and gyrotactic microorganisms past a stretching sheet. The fluid flow is assumed to be laminar and incompressible. The fluid flow is considered to be highly magnetized by applying a strong magnetic field. Newtonian viscous dissipation, chemical reactions, and Arrhenius activation energy are taken into consideration. The transformed system of equations is solved by HAM. Convergence analysis of the HAM is displayed with the help of figures. The relations of physical factors with fluid flow profiles are displayed with the help of figures and tables. It is reported that the greater material and mixed convection factors have escalated the fluid’s velocity. The higher Eckert number and thermal conductivity constant have augmented the thermal function, while the higher Prandtl number has reduced the temperature profile. The greater activation energy factor has augmented the concentration profile, while the augmenting chemical reaction and Schmidt number have reduced the concentration profile. In the streamlines of the steady and unsteady flows, there is also a significant difference in behavior.

Performance of Dual Viscoelastic Wave Barrier System with Unequal Draft

This work investigated the interaction of surface waves with a dual-barrier system comprising two vertical viscoelastic thin sheets with variable spacing in finite water depth without preassumption of its dynamic behavior. The two sheets were assumed to be made of the same material and under different tensions, and both penetrated into the water depth partially with unequal drafts. The viscoelastic behavior of the sheet material, which accounts for its elastic deformation and internal energy dissipation, is represented by the Voigt model. Using the eigenfunction expansion and least square determination, analytical solutions were obtained for the dual-barrier system, including the asymptotic case of a single sheet when the second sheet draft approaches zero. Subsequently, the effects of hydroelastic regimes and viscoelasticity were examined. With the single-sheet system, the wave transmission decreases as the tensioned sheet shifts from platelike to membranelike, and its material has higher internal energy dissipation (i.e., viscosity). When the size of the bottom opening increases to a gap ratio larger than ∼0.6, however, the wave transmission becomes dominated by the diffraction through the gap, and the influence of sheet material characteristics is no longer significant. With the double-sheet system, the results show that the performance of the wave barrier improves significantly by the presence of the second sheet, even with a small draft. Complex resonating patterns can be observed with increase in sheet spacing for the dual-barrier system, which reduces the wave transmission. The presence of viscosity of the double-sheet system dampens the resonance, but also reduces the wave transmission by itself through the viscous dissipation of the incident wave energy.

Theoretical study on the dynamic compression and energy absorption of porous materials filled with magneto-rheological fluid

In this paper, the dynamic compression and energy absorption behaviours of porous materials filled with MR fluid are studied theoretically. By means of Darcy's law, Ergun's equation and energy method, the single-layer and two-layer models for the energy absorption and dynamic stress are first derived, in which the compression of the skeletal material, the inertia effect, viscous flowing of the fluid as well as the MR effect are considered. The comparisons between the theoretical results and previous experiments of porous copper specimens show that the two-layer model can predict the dynamic stress before the circumferential failure of specimen very well. Based on the theoretical models, it is found that the energy dissipated by the deformation of the skeletal material and MR effect is nearly insensitive to the strain-rate, while that by the viscous flowing and inertial effect increases linearly and quadratically with the increase of impact velocity, respectively. When the strain rate is low, the energy dissipation due to the MR effect is larger than that by viscous flowing. However, if the strain-rate is higher than a certain value, the viscous energy dissipation will be dominant. Moreover, with the same strain rate, specimens with larger radius/thickness ratio could obtain higher compression stress. To improve the controllability of the MR fluid-filled porous material, higher yield stress induced by magnetic field is preferred, and the strain-rate should be as low as possible.

Viscous energy dissipation reduction by optimization of multiple shapes

AbstractShape optimization has been an active field of research for the past decades and is used especially in engineering. On this poster, we consider a shape optimization model with multiple shapes, i.e., we consider more than one shape to be optimized. We assume that the optimization variable is a set Γ = (Γ1,…, ΓN) of non‐intersecting shapes contained in a bounded domain D ⊂ ℝd. We note that D depends on Γ, i.e., D = D(Γ). On this poster, a shape optimization of a two‐dimensional fluid‐mechanical problem is considered. We minimize the viscous energy dissipation in the fluid domain D, more precisely urn:x-wiley:16177061:media:PAMM202100261:pamm202100261-math-0001 subject to the equations describing Stokes flow urn:x-wiley:16177061:media:PAMM202100261:pamm202100261-math-0002 urn:x-wiley:16177061:media:PAMM202100261:pamm202100261-math-0003 with appropriate boundary conditions, where y ∈ ℝ2 describes the fluid velocity, p ∈ ℝ the pressure, and f ∈ ℝ2 a given source term. In order to solve the minimization problem, we use an optimization approach based on the Steklov‐Poincaré metric, where the so‐called weak form of the shape derivative can be used. The algorithm and implementation details are presented, and numerical results are discussed for the optimization of multiple shapes in the fluid domain.

Innovative hybrid device for the simultaneous damping of pressure pulsations and vibrations in positive displacement compressor manifolds

Manifold vibrations in refrigerating compressor manifolds are the result of pressure pulsations as well as compressor-generated mechanical vibrations. In this article, an analysis of a device combining a TMD (tuned mass damper) and a shaped nozzle for pressure pulsation attenuation is presented. The nozzle shape and geometry is determined on the basis of our previous findings using 3D analysis. The nozzle pulsation attenuation is caused by viscous and vorticity energy dissipation. The nozzle is mounted inside the pipe in the chosen position using springs with tuned stiffness. The nozzle mass and spring stiffness create the TMD. The simulation of the TMD damping using the OpenModelica SimulationX package is presented with kinetic energy transfer from a vibrating pipe to the TMD. It transpired that the result on the pressure pulsations damping of the vibrating nozzle is not as high as it is in the case of a nozzle in a fixed position due to the clearance between the nozzle and the pipe that is necessary in the TMD case. Nevertheless, vibrations are more efficiently damped using the combined TMD and nozzle damping action (28%) than a fixed nozzle (13%). This innovation makes it possible to reduce vibration and pressure pulsation using one device, which is especially important for small refrigerating manifolds, where the size of the damping element is important and vibration reduction leads to noise attenuation. The hybrid suppression device is currently patent pending.

Investigation of mixed convection magnetized Casson nanomaterial flow with activation energy and gyrotactic microorganisms

Present article addresses mixed convection magnetohydrodynamic Casson nanomaterial flow by stretchable cylinder. The effects of thermal, solutal and motile density stratifications at the boundary of the surface are accounted. Flow governing expressions are acquired considering aspects of permeability, thermal radiation, chemical reaction, viscous dissipation and activation energy. The obtained flow model is made dimensionless through transformations and then tackled by NDsolve code in Mathematica. Physical impacts of sundry variables on nanomaterial velocity, temperature distribution, volume fraction of microorganisms and mass concentration is investigated through plots. Furthermore, quantities of engineering interest like surface drag force, heat transfer rate, density number and Sherwood number are computed and analyzed. We observed that fluid velocity diminishes for higher curvature variable, Casson fluid material variable, Hartmann number and permeability parameter. Fluid temperature has a direct relation with Eckert number, thermophoresis variable, Brownian dispersal parameter, Prandtl number and Hartmann number. Volume fraction of gyrotactic microorganisms is decreasing function of bioconvection Lewis number, stratification parameter and bioconvection Peclet number. Detailed observations are itemized at the end.

Flow Dynamics in a Model of a Left Ventricle with Different Mitral Valve Orientations

The formation of vortex rings at valve leaflets during ventricular inflow has been a topic of interest for many years. It is generally accepted nowadays that the purpose of vortex rings is to conserve energy, reduce the workload on the heart, and minimize particle residence time. We investigated these claims by testing three different levels of annulus angle for the mitral valve: a healthy case, a slightly angled case (20°), and a highly angled case (46°). Circulation was determined to be reversed in the non-healthy case, with a dominant counterclockwise rotation instead of clockwise. Viscous energy dissipation was highest in the slightly angled case, followed by the healthy case and then the highly angled case. A Lagrangian analysis demonstrated that the healthy case resulted in the least amount of stasis, requiring eight cardiac cycles to evacuate 99% of initial ventricle volume compared to the 16 and 13 cardiac cycles required by the slightly angled and highly angled cases, respectively.

Determination of critical testing frequency of the short fiber‐reinforced plastics for efficient fatigue test

AbstractHeat generated by viscous energy dissipation and friction during high‐frequency fatigue testing can reduce the fatigue life of short fiber‐reinforced plastics. Herein, we proposed new method of determining an appropriate testing frequency, taking into consideration the temperature increase in SFRPs during fatigue testing. An experimental procedure was developed to obtain viscoelastic and thermal parameters in a theoretical model using dynamic mechanical analyses and fatigue tests with an infrared camera. Then, according to the stress levels under tension in fatigue tests, a critical frequency was calculated to allow a temperature increase within 10°C. Finally, experimental fatigue tests at low stress levels and high frequencies were performed, demonstrating the applicability of the current method to design fatigue tests that take into account stress levels at a given frequency and a limited temperature rise.

Analysis of dynamic properties and transitional failure of clay–sand mixture in fine-grained soil based on mineral composition

Reexamining the transitional failure with energy method is a new idea of studying the dynamic properties of fine-grained soil. In this paper, a series of undrained cyclic triaxial tests and low-vacuum environmental scanning electron microscopy were employed to study the dynamic properties of two types of clay–sand mixtures with a similar plasticity index at a fine-grained content of 70%. In terms of mineral composition, Toyoura sand constituted the coarse-grained fraction of the clay–sand mixture, and its fine-grained portion was comprised of different mass ratios of quartz, albite, Na-montmorillonite, and kaolinite (Qc:Ac:Mc:Kc); that is, the specimens were divided into groups T-Q42.5A42.5M0K15 and T-Q45A45M2.5K7.5. The results showed that T-Q42.5A42.5M0K15 with an embedded dispersed fabric had a failure mode dominated by the pore water pressure, so it had an inferior cyclic strength compared to T-Q45A45M2.5K7.5 with an embedded flocculated fabric. Meanwhile, the dimensionless viscous energy dissipation ratio (VEDR) was introduced to observe the history of the differential energy dissipation of the clay–sand mixture and thus reveal the limitations of the plasticity index for the evaluation of the dynamic properties of soil. Furthermore, compared with previously studied artificial marine clay with a clay-like mode of VEDR and low-plasticity fine-grained tailings with a sand-like mode of VEDR, the clay–sand mixture studied herein offered a transitional mode of VEDR. On the whole, this work can make a significant contribution to the research on transitional failure by demonstrating that traditional dynamic properties and energy dissipation can act together as the indicators of the dynamic behavior of soil.

Effects of Clay Mineral Composition on the Dynamic Properties and Fabric of Artificial Marine Clay

Marine clays are easily affected by different mineral composition in cyclic load-based geological hazards. Therefore, based on analyzing the mineral composition of natural marine clay, it is the key to predict the dynamic properties of natural materials under cyclic loading by using quantitated artificial marine clay. In this study, the marine clay found in the South China Sea deltas was investigated. Based on the results of geological conditions and mineral composition analyses, raw non-clay minerals (such as quartz, albite) and clay minerals (such as Na-montmorillonite and kaolinite) were used to produce artificial marine clay, the dynamic properties of which were studied from the impact of mineral composition. Dynamic triaxial laboratory testing for artificial marine clay comprising various clay minerals was performed under identical test conditions. The artificial marine clay with high montmorillonite content exhibited slower development of strain, more sluggish growth in pore water pressure, more rounded hysteresis curves, greater stiffness, and more prolonged viscous energy growth than the clay with low montmorillonite content. In addition, the flocculated fabric of the artificial marine clay with high montmorillonite content demonstrated sufficient pore space changes, more uniform pore distribution, and larger specific surface area than the dispersed fabric of the clay with low montmorillonite content. The factors arising from the influence of montmorillonite may lead to microstructural and fabric changes, hinder the development of pore water, and increase intergranular contact stiffness as well as delay the cyclic strain amplitude at the breakpoint of viscous energy dissipation. In general, the results presented in this study confirm that clay minerals, especially montmorillonite, have significant influence on the dynamic properties of large strain.

Viscous dissipation in the heat transfer between a rotating cylinder and viscous media under forced convection

The effects of viscous energy dissipation on the forced convection heat transfer between an unconfined rotating isothermal circular cylinder and surrounding viscous fluids are numerically investigated. The heat transfer characteristics are investigated for the range of conditions of the Reynolds number Re = 1-40, Prandtl number Pr = 1-100 (the Peclet number ranges between 1 and 4000), dimensionless rotational velocities α = 0-3, and Brinkman number Br = 0-1. For the steady flow regime, the isotherm patterns are presented for the range of values of Reynolds number, Brinkman number, Prandtl number, and rotational velocity. For low Peclet numbers (Re×Pr), the heat generated by the viscous dissipation is not efficiently removed which, promotes the appearance of hot spot zones. The variation of the local and average Nusselt numbers on the cylinder surface shows the effects of Brinkman number, Prandtl number, and rotational velocity on heat transfer between a rotating isothermal cylinder and a viscous flow for the range of conditions studied.