Quiescent Medium Research Articles

Dual solutions for second-order slip flow and heat transfer on a vertical permeable shrinking sheet

The aim of the paper is to study viscous fluid flow and heat transfer with second-order slip at linearly shrinking isothermal sheet in a quiescent medium. The sheet is permeable and subjected to constant suction. The governing equations consisting of the continuity, momentum, and the energy are transformed into a system of ordinary differential equations using suitable similarity transformation and solved numerically using the Runge–Kutta fourth-order method with the shooting technique. It is found that the problem possesses a dual physical solution. The effects of different parameters on the velocity and the temperature distributions as well as the skin-friction coefficient and the Nusselt number are presented graphically and in tabular form.

Free Convective Flow of Non-Newtonian Nanofluids in Porous Media with Gyrotactic Microorganism

The two-dimensional steady laminar boundary-layer free convective flows along an isothermal solid horizontal flat plate located in a porous quiescent medium filled with non-Newtonian power law nanofluids that contain both nanoparticles and gyrotactic microorganisms are investigated numerically. The horizontal plate has uniform surface temperature, solute, nanoparticle concentrations and density of the motile microorganism. The governing partial differential equations are nondimensionalized, and then similarity transformations are developed using a linear group of transformations. Using similarity transformation, the governing equations are reduced to a system of nonlinear ordinary differential equations, which are solved numerically. The influence of controlling parameters on the dimensionless velocity, temperature, nanoparticle concentration, and density of motile microorganisms, as well as the local Nusselt, Sherwood, and motile microorganism numbers, are studied. It is found that the bioconvection parameters have strong effects on the flow, heat and mass transfer, and motile microorganism numbers. An excellent agreement is found between numerical results of the study with published results in the open literature for special cases.

Anomalous field-induced growth of fluctuations in dynamics of a biased intruder moving in a quiescent medium

We present exact results on the dynamics of a biased, by an external force F, intruder (BI) in a two-dimensional lattice gas of unbiased, randomly moving hard-core particles. Going beyond the usual analysis of the force-velocity relation, we study the probability distribution P(R(n)) of the BI displacement R(n) at time n. We show that despite the fact that the BI drives the gas to a nonequilibrium steady state, P(R(n)) converges to a Gaussian distribution as n→∞. We find that the variance σ(x)(2) of P(R(n)) along F exhibits a weakly superdiffusive growth σ(x)(2)~ν(1)nln(n), and a usual diffusive growth, σ(y)(2)~ν(2)n, in the perpendicular direction. We determine ν(1) and ν(2) exactly for arbitrary bias, in the lowest order in the density of vacancies, and show that ν(1)~|F|(2) for small bias, which signifies that superdiffusive behavior emerges beyond the linear-response approximation. We also present analytical arguments predicting a striking field-induced superdiffusive behavior σ(x)(2)~n(3/2) for two-dimensional stripes and three-dimensional capillaries, which is confirmed by Monte Carlo simulations.

Numerical simulation of an energy deposition zone in quiescent air and in a supersonic flow under the conditions of interaction with a normal shock

The potential of using the Euler equations to numerically simulate the evolution of localized energy deposition zones interacting with a normal shock in quiescent air and in a supersonic channel flow is demonstrated. Simulation results are compared with available experimental data for an optical discharge in quiescent air and with results calculated for a supersonic flow using the Navier-Stokes equations with allowance for real gas effects. The possibility of predicting gasdynamic effects using the T- and q-models of energy deposition for perfect gas is justified. The variation of the gasdynamic structure and flow parameters near an energy deposition zone developing in a quiescent medium and interacting with a normal shock is analyzed in detail for different energy deposition powers.

Temporal multiscale approach for nanocarrier motion with simultaneous adhesion and hydrodynamic interactions in targeted drug delivery

We present a fluctuating hydrodynamics approach and a hybrid approach combining fluctuating hydrodynamics with generalized Langevin dynamics to resolve the motion of a nanocarrier when subject to both hydrodynamic interactions and adhesive interactions. Specifically, using these approaches, we compute equilibrium probability distributions at constant temperature as well as velocity autocorrelation functions of the nanocarrier subject to thermal motion in a quiescent Newtonian fluid medium, when tethered by a harmonic spring force mimicking a tether due to a single receptor–ligand bond. We demonstrate that the thermal equipartition of translation, rotation, and spring degrees of freedom are preserved by our formalism while simultaneously resolving the nature of the hydrodynamic correlations. Additionally, we evaluate the potential of mean force (or free energy density) along a specified reaction coordinate to facilitate extensive conformational sampling of the nanocarrier motion. We show that our results are in excellent agreement with analytical results and Monte Carlo simulations, thereby validating our methodologies. The frameworks we have presented provide a comprehensive platform for temporal multiscale modeling of hydrodynamic and microscopic interactions mediating nanocarrier motion and adhesion in vascular targeted drug delivery.

Natural convection in power-law fluids from a tilted square in an enclosure

In this study, laminar natural heat transfer from a heated tilted square (two-dimensional) to a quiescent power-law medium filled in a square enclosure has been investigated numerically. In particular, the coupled momentum and energy equations have been solved numerically over the range of kinematic conditions as: Grashof number, 102⩽Gr⩽105; Prandtl number, 0.71⩽Pr⩽100 and power-law index, 0.2⩽n⩽1.5. In addition, the effect of the two commonly employed thermal boundary conditions, namely, that of the constant temperature or constant heat flux on the surface of the tilted bar is also examined. However, the results reported herein are restricted to three relative positions of the heated bar on the vertical mid-plane of the enclosure, namely, β2=0.25, 0.5 and 0.75 whereas the side of the enclosure is four times the size of the heated cylinder. Depending upon the placement of the heated cylinder with respect to the bottom of the enclosure, one may observe single- or double-celled flow patterns. Overall, the influence of the power-law fluid behavior is strongly modulated by the values of the Grashof number (Gr), Prandtl number (Pr) and the relative positioning of the cylinder (β2). The detailed flow and temperature fields are visualized in terms of the streamline and isotherm contours. The heat transfer characteristics are interpreted in terms of the local Nusselt number on the surface of the heated cylinder and the overall gross behavior is denoted in terms of the average Nusselt number. Finally, the numerical results obtained in this work have been correlated as functions of the Grashof number, Prandtl number, power-law index and the relative positioning of the heated cylinder.

A Numerical Investigation on Dynamics and Breakup of Liquid Sheet

The details on dynamics and breakup processes of liquid sheets are numerically investigated by considering two liquid sheet arrangements: the contraction of liquid sheet in a still quiescent gas medium, and a moving liquid sheet in a gas medium of much higher velocity compared with the liquid sheet. The first part of the study reveals that the surface tension forms the capillary wave on the liquid sheet surface. By extensive calculation, it is conformed that only surface tension force cannot disintegrate the liquid sheet. The dragging of liquid by co-flowing gas is very important for the occurrence of sheet breakup. To prove this concept, the second part of the investigation is performed, which reveals the details of breakup processes. Two effects are observed: the aerodynamic effect and the surface tension effect. The main function of the aerodynamic effect is to stretch the liquid sheet by drag force and create the steps on the sheet surface which is then followed by a pair of vortices and stagnation point prior to the end of every step. When the thickness of the sheet becomes thin enough, the dragging of liquid by the gas flow at the upstream of the neck part of the bulbous tip causes formation of a pair of vortices and stagnation point on the thin portion of the liquid sheet restricts the liquid flow and eventually the breakup occurs.

On the Evolution of a Plain Zero Net Mass Flux Jet Injected in a Quiescent Medium

A plain zero net mass flux (ZNMF) jet injected in a quiescent medium is presently investigated numerically employing the unsteady Reynolds averaged Navier Stokes simulation approach. The flow features encompassing centerline mean velocity evolution, self-similar mean velocity distribution, jet momentum flux and stagnation point location are studied at different jet Strouhal and Reynolds numbers. The present investigation shows that the far field behavior of a plain ZNMF jet somewhat resembles the steady plain turbulent jets. Accordingly, the centerline mean velocity varies on the basis of a power law decaying profile and the cross stream mean velocity distribution illustrates an approximately self-similarity condition. However, it is demonstrated that the present ZNMF jet momentum flux is not constant with the streamwise coordinate contrary to a steady turbulent jet. Also, the stagnation point location is shown to reach its maximum at around t/T = 0.8 and the maximum location strongly depends on the jet Strouhal number.

Crystallization-in-emulsion process of a melted organic compound: In situ optical monitoring and simultaneous droplet and particle size measurements

The crystallization-in-emulsion process allows the production of solid particles exhibiting specific features. Here, the batch crystallization process carried out by cooling a melted oil dispersed as an oil-in-water emulsion was studied. Two experimental set-ups allowing the in situ visualization of the nucleation and growth phenomena occurring in the dispersed liquid phase were developed. Observations in quiescent medium of motionless droplets having a diameter of few tens of micrometers showed that primary nucleation started on the inner surface of the droplets. The fast growth of the crystals consumed all the liquid contained within each droplet and was confined within each droplet by the oil–water interface. Solid polycrystalline particles similar in size to the parent droplets were produced. Dynamic tracking of the transient evolution of the size distributions of the two populations of droplets and solid particles during the cooling process in a stirred vessel was carried out using an in situ optical probe. It was shown that the droplets crystallized very progressively during cooling, starting with the largest droplets and ending with the smaller size droplets since the induction time of primary nucleation was dependent on droplet volume. In dilute conditions (1%wt% of dispersed phase) each droplet was converted into a single solid particle. Secondary nucleation based on inter-droplet collisions was not observed in these conditions.

ICE AND DUST IN THE QUIESCENT MEDIUM OF ISOLATED DENSE CORES

The relation between ices in the envelopes and disks surrounding YSOs and those in the quiescent interstellar medium is investigated. For a sample of 31 stars behind isolated dense cores, ground-based and Spitzer spectra and photometry in the 1-25 um wavelength range are combined. The baseline for the broad and overlapping ice features is modeled, using calculated spectra of giants, H2O ice and silicates. The adopted extinction curve is derived empirically. Its high resolution allows for the separation of continuum and feature extinction. The extinction between 13-25 um is ~50% relative to that at 2.2 um. The strengths of the 6.0 and 6.85 um absorption bands are in line with those of YSOs. Thus, their carriers, which, besides H2O and CH3OH, may include NH4+, HCOOH, H2CO and NH3, are readily formed in the dense core phase, before stars form. The 3.53 um C-H stretching mode of solid CH3OH was discovered. The CH3OH/H2O abundance ratios of 5-12% are larger than upper limits in the Taurus molecular cloud. The initial ice composition, before star formation occurs, therefore depends on the environment. Signs of thermal and energetic processing that were found toward some YSOs are absent in the ices toward background stars. Finally, the peak optical depth of the 9.7 um band of silicates relative to the continuum extinction at 2.2 um is significantly shallower than in the diffuse interstellar medium. This extends the results of Chiar et al. (2007) to a larger sample and higher extinctions.

Liquid Droplet Growth from a Punctured Vessel Under Steady Flow Conditions

The liquid droplet growth from a punctured, pressurized vessel immersed in a quiescent medium is studied under steady flow conditions. Local strain rates at the puncture site are also investigated. The droplet growth and local strain rates at the puncture are characterized as functions of various hydrodynamic and geometric conditions. Dimensional analysis shows that the fractional droplet growth rate, Q*, is a function of the Reynolds number, Weber number, hole-to-main tube diameter ratio, D*, and the puncture geometry. A 3-D finite volume computational model is constructed for laminar flow of a Newtonian fluid under steady conditions and validated with supporting experiments. The results show that the fractional growth rate Q* increases with the Weber number and is largest for the lowest Reynolds number of one. In addition, the droplet shape is spherical at low Weber numbers (2.6) and ellipsodial at high Weber numbers (7.8). Additional simulations detail how the growth ratio is lower for small diameter ratios and rectangular punctures. Physiological implications for the hemostatic response (clotting) of a punctured blood vessel can be found by examining the local strain rates in the vicinity of the puncture. The strain rate displays the largest values for the highest Reynolds number (100). In addition, when D* = 0.04 the strain rate is greater at the low (2.6) and high (7.8) Weber numbers, while the strain rate is larger for D* = 0.075 when the Weber number is 5.2. The strain rate is also affected by the puncture shape and displays higher values for the rectangular puncture when Weber < 5.2. Finally, the impact of microgravity on droplet formation was studied. Numerical simulations and quantification of the forces on fluid particles show that there is no effect from gravity on the droplet growth rate or strain rate in medium and large sized veins.

Bias- and bath-mediated pairing of particles driven through a quiescent medium

A particle driven by an external force in a molecular crowding environment - a quiescent bath of other particles, makes their spatial distribution inhomogeneous: the bath particles accumulate in front of the biased particle (BP) and are depleted behind. In fact, a BP travels together with the inhomogeneity it creates. A natural question is what will happen with two BPs when they appear sufficiently close to each other such that the inhomogeneities around each of them start to interfere? In quest for the answer we examine here, via Monte Carlo simulations, the dynamics of two BPs in a lattice gas of bath particles. We observe that for a sufficiently dense medium, surprisingly, both BPs spend most of the time together which signifies that the interference of the microstructural inhomogeneities results in effectively attractive interactions between them. Such statistical pairing of BPs minimizes the size of the inhomogeneity and hence reduces the frictional drag force exerted on the BPs by the medium. As a result, in some configurations the center-of-mass of a pair of BPs propagates faster than a single isolated BP. These jamming-induced forces are very different from fundamental physical interactions, exist only in presence of an external force, and require the presence of a quiescent bath to mediate the interactions between the driven particles.

Numerical Simulation of Pressure-Swirl Spray Dispersion by Using Eulerian-Lagrangian Method

To gain a general understanding of atomization and sheet breakup processes, the interaction of pressure-swirl hollow-cone sprays and a quiescent medium was investigated computationally. The spray characteristics of Iso-octane (n-C8H18) with high pressure-swirl injector in the ambient conditions are modeled. The Linearized Instability Sheet Atomization (LISA) model has been used to describe the primary breakup processes of the spray. Sauter Mean Diameter, sheet thickness and exit velocity were computed as the results of primary breakup. Disintegration of large drops is simulated using Taylor analogy breakup (TAB) model in which the Rosin-Rammler distribution is used. Evaporation and collision models are deactivated in this study. The model considers the transient behavior of the pre-spray and steady-state behavior of the main spray for three various injection pressures and liquid mass flow rates. Qualitative and quantitative comparisons between the simulated and experimentally measured results were made. The numerical simulations can successfully demonstrate the spray characteristics, such as spray tip penetration, drop sizes and overall spray structure.

Quantitative schlieren measurements in a normal incidence acoustic impedance tube

Historically, the schlieren-based optical deflectometer has been successfully used to characterize high-speed compressible flows. This article describes the use of the instrument to measure significantly smaller density gradients associated with the one-dimensional acoustic wave field in a quiescent medium inside a plane wave tube. Results of the static calibration are presented. Cross-spectral analysis between the light intensity fluctuations in a schlieren image and a reference microphone signal is then used to determine the quantitative density gradient field in the normal incidence impedance tube. The results are rigorously compared with those obtained using the standard two-microphone method. The lowest sound pressure level measured with reasonable accuracy is a 100 dB (re 20 μPa), 5 kHz tone. Expressions for the sensitivities of both the optical system and the photodetector device are derived, as well as an expression for the minimum detectable signal. These results are used to discuss potential improvements and fundamental limitations.

New effects of stratified gas detonation

28 In this paper, we consider problems on initiated detonation in a supersonic flow and in a quiescent sto� ichiometric propane-air mixture that partly or entirely fills in the cross section of a plane channel. In this flow, the detonation initiation occurs due to a shelf or a wall completely closing the channel, whereas in a quiescent medium, an explosion is used. The study is conducted in the framework of the singlestage com� bustion kinetics by the numerical method based on Godunov's scheme. We have also determined the crit� ical conditions for the detonation initiation, which are associated with both the incidentflow velocity and the explosion energy. In all processes under consideration, we found the mechanism of the detonation propaga� tion, which had not been known previously. The mechanism is stipulated by the formation of a compli� cated waveflow structure. For this structure, the pen� etration of the shock wave propagating through inert gas into the layer ahead of the detonation wave is char� acteristic. As a result, inert gas is heated and inflamed. Thus, the process is of a periodic nature that differs from the usual cellular detonation in a homogeneous

The Dynamics of Periodically Forced Prolate Spheroids in a Quiescent Newtonian Fluid with Weak Inertia

The effects of convective and unsteady inertia on the dynamics of periodically forced neutrally buoyant prolate spheroids in a quiescent Newtonian fluid medium, at low Reynolds numbers have been modeled. The resulting nonlinear equations have been solved using appropriate numerical methods. Several tests including a perturbation analysis are performed to validate results. A preferred direction, which is identified as the initial direction of motion, is observed that manifests itself in the properties of the solution. Results of the behavior of various parameters with respect to the Reynolds number, aspect ratio of the spheroid and the amplitude of the periodic force are presented. The results are technologically important as they may lead to insights in the development of active dampeners and smart fluids.

A Quadratic Spline based Interface (QUASI) reconstruction algorithm for accurate tracking of two-phase flows

A new Quadratic Spline based Interface (QUASI) reconstruction algorithm is presented which provides an accurate and continuous representation of the interface in a multiphase domain and facilitates the direct estimation of local interfacial curvature. The fluid interface in each of the mixed cells is represented by piecewise parabolic curves and an initial discontinuous PLIC approximation of the interface is progressively converted into a smooth quadratic spline made of these parabolic curves. The conversion is achieved by a sequence of predictor–corrector operations enforcing function ( C 0) and derivative ( C 1) continuity at the cell boundaries using simple analytical expressions for the continuity requirements. The efficacy and accuracy of the current algorithm has been demonstrated using standard test cases involving reconstruction of known static interface shapes and dynamically evolving interfaces in prescribed flow situations. These benchmark studies illustrate that the present algorithm performs excellently as compared to the other interface reconstruction methods available in literature. Quadratic rate of error reduction with respect to grid size has been observed in all the cases with curved interface shapes; only in situations where the interface geometry is primarily flat, the rate of convergence becomes linear with the mesh size. The flow algorithm implemented in the current work is designed to accurately balance the pressure gradients with the surface tension force at any location. As a consequence, it is able to minimize spurious flow currents arising from imperfect normal stress balance at the interface. This has been demonstrated through the standard test problem of an inviscid droplet placed in a quiescent medium. Finally, the direct curvature estimation ability of the current algorithm is illustrated through the coupled multiphase flow problem of a deformable air bubble rising through a column of water.

Performance Evaluation of a Micro Synthetic-Jet Actuator via Its Generated Vortices

The performance of a two-dimensional micro synthetic jet actuator is evaluated using computational modeling and simulation. A synthetic jet is a zero net mass flux device having a cavity with an oscillating membrane as a sidewall. The motion of the membrane produces a fluctuating jet flow, which transfers linear momentum to the external domain. A Navier-Stokes solver that can run on moving and deforming meshes is used to study the membrane-driven flow in and out of the micro cavity geometry. The primary focus of the present investigation is on the delineation of a feasible design space defined by the geometric and actuation parameters that directly affect its performance. The design variables are selected to be the membranes oscillation frequency and amplitude, the orifices width and height, and the cavitys width and height. The results clearly indicate that, for a micro synthetic jet discharging into a quiescent medium, these variables have significant control on the vortex formation, its size, its circulation and its momentum flux. Therefore, the desired actuation can be obtained by manipulating these design variables. Keywords: Micro synthetic jet, parametric study, performance

Chemodynamical evolution of gas near an expanding HII region

A self-consistent model for the chemical-dynamical evolution of a region of ionized hydrogen around a massive young star and of the surrounding molecular gas is presented. The model includes all main chemical and physical processes, namely the photoionization of atomic hydrogen, photodissociation of molecular hydrogen and other molecules, and the evaporation of molecules from the mantles of dust particles. Heating and cooling processes are taken into account in the temperature calculations, including cooling in molecular and atomic lines. The hydrodynamical equations were solved using the Zeus2D hydrodynamical software package. This model is used to analyze the expansion of a region of ionized hydrogen around massive stars (effective temperature of 30 000 and 40 000 K) in a medium with various initial density distributions. The competition between evaporation from dust mantles and the photodissociation of molecules results in the formation of a transition layer between the hot HII region and cool quiescent medium, characterized by high abundances of molecules in the gas phase. The thickness of the transition layer is different for different molecules. Since there is a velocity gradient along the transition layer, and the maxima in the distributions of different molecules are at different distances from the star, observations of molecular emission lines should reveal distinction in shifts of lines of different molecules relative to the velocity of the quiescent gas. Such shifts have indeed been detected during molecular observations of the region of ionized hydrogen Sh2-235. For an initial gas density of 103 cm−3, the increase in the abundances of H2O and H2CO in the transition layer after desorption from dust occurs gradually rather than in a jump-like fashion; therefore, the concept of a “evaporation front” can be used only formally. In addition, the distances between the evaporation fronts for different molecules are significant. At higher initial gas densities (104 cm−3), sharp evaporation fronts are formed for the different molecules, which are close to each other and to the shock front. In this case, it is possible to speak of a single evaporation front for CO, H2O, and H2CO.

Detailed flow physics of the supersonic jet interaction flow field

The supersonic jet interaction flow field generated by a sonic circular jet with a pressure ratio of 532 exhausting into a turbulent MACH 4.0 cross flow over a flat plate was investigated using numerical simulations. The simulations made use of the three-dimensional Reynolds-averaged Navier–Stokes (RANS) equations coupled with Wilcox’s 1998 k-ω turbulence model. The numerical solution was validated with experimental data that include the pressure distribution on the flat plate, with an empirical formula for the height of the barrel shock, and with the Schlieren pictures showing the location and shape of the main shock formations. The simulations correctly captured the location and shape of the main flow features and compared favorably with the experimental pressure distribution on the flat plate. The validated numerical simulation was used to investigate in detail the flow physics. The flow field was found to be dominated by the shock formations and their coupling with the strong vortical structures. Three primary shock formations were observed: a barrel shock, a bow shock, and a separation-induced shock wave. While the general structure of the barrel shock was found to be similar to that of the underexpanded jet exhausting into a quiescent medium, two unique features distinguished the flow field: the concave indentation in the leeside of the recompression (barrel) shock and the folding of the windward side of the barrel shock due to an inner reflection line. The presence of the steep pressure gradients associated with the shocks creates strong vortical motions in the fluid. Six primary vortices were identified: (i) the well-known horseshoe vortex, (ii) an upper trailing vortex, (iii) two trailing vortices formed in the separation region and, aft of the bow shock wave, (iv) two more trailing vortices that eventually merge together into one single rotational motion. The low-pressure region aft of the injector was found to be generated by the combined effect of the concave indentation in the leeside of the barrel shock and the lower trailing vortices. The trailing vortices were found to be the main mechanism responsible for the mixing of the injectant with the freestream fluid.