Rectilinear Flow Research Articles

Improving the separation efficient of particles smaller than 2.5 micrometer by combining ultrasonic agglomeration and swirling flow techniques.

The method for increasing the separation efficiency of particles smaller than 2.5 micrometers by combined ultrasonic agglomeration and swirling flow technique is proposed in the article. The swirling flow creates areas with an increased concentration of particles on the outer radius of the vortex. The ultrasonic exposure on these areas leads to more efficient agglomeration and the formation of agglomerates of many times larger than the original particles. The resulting agglomerates are easily separated from the gas flow. The design of the agglomerator was developed. The vortex velocity is determined, at which ultrasonic exposure on the swirling flow increases the average particle size d32 = 2.5 micrometer to 4.5 times. The ultrasonic exposure on a rectilinear flow can increase the particle size no more than 1.6 times for comparison. The proposed method is compared with inertial gas clearing in a cyclone. It was found that the proposed combined method allows increasing the cleaning efficiency from 46% to 85% at ultrasonic exposure on the swirling flow in the agglomerator and cyclone.

How to extract the angle attack on airfoils in cycloidal motion from a flow field solved with computational fluid dynamics? Development and verification of a robust computational procedure

One of the key problems faced by researchers dealing with Computational Fluid Dynamics simulations and rotating machines is represented by how to extract the angle attack from a numerically computed flow field. If this issue has been addressed successfully for some applications, in case of airfoils moving in cycloidal motion (i.e. having a rotational motion within a rectilinear flow field, like in Darrieus Vertical-Axis Wind Turbines) some proposals do exist, but always affected by some arbitrary choices on the velocity probing that are not supported by a proper verification. The aim of the present study is to try finding a robust computational procedure tailored for the scope. To this end, three different post-processing methods - detailed in the study – were considered and applied to the flow fields of 2-blade H-Darrieus rotor, coming from a high-fidelity unsteady model based on Computational Fluid Dynamics; the resulting blade angle of attack trends over one rotor revolution were then combined with available blade forces data to assess the corresponding lift and drag coefficients. In order to assess the actual accuracy of these approaches for a stable tip-speed ratio, the post-processed force coefficients were compared to the ones computed via a numerical pitching airfoil model, which received the sampled angle of attack trends as input; eventually, the pitched lift and drag values have been used to reconstruct the blade forces over one rotor revolution and compare them with the ones coming from full turbine simulations. Results show large scattering of obtained data, remarking the importance of the proper selection of the angle of attack sampling strategy for the analysis of turbine performance. Overall, the “LineAverage” approach, i.e. the use of multiple sampling points around the airfoil for velocity probing, has proved to be the most accurate method.

Improving the performance of air purification efficiency from fine-dispersed particles by ultrasonic exposure in swirling flow

The article presents the results of a research of the process of removing particles in range 2.5 µm that are most dangerous to human health using ultrasonic coagulation. The two-stage gas clearing system consisting of the agglomerator and the cyclone dust collector (supplemented by an ultrasonic radiator) was proposed and made. The carried out investigations have revealed the optimal conditions for the formation of a swirling flow, providing high efficiency coagulation of fine-dispersed particles. The formation of a swirling gas-dispersed flow in the conditions of ultrasonic exposure provides an increase in the average particle size 2.5 µm by 4.5 times due to particles convergence and the formation of local areas with high concentration. In this case, the ultrasonic effect on a rectilinear flow with 2.5-μm particles allows increasing particles size of only 1.6 times. The ultrasonic exposure has increasing 2.5-µm particle clearing efficiency from 46 to 85% by optimal conditions for gas-dispersed flow.

On the stability of waves in classically neutral flows

AbstractThis paper reports a breakdown in linear stability theory under conditions of neutral stability that is deduced by an examination of exponential modes of the form $h\approx{{e}^{i(kx-\omega t)}}$, where $h$ is a response to a disturbance, $k$ is a real wavenumber and $\omega (k)$ is a wavelength-dependent complex frequency. In a previous paper, King et al. (2016, Stability of algebraically unstable dispersive flows. Phys. Rev. Fluids, 1, 073604) demonstrates that when Im$[\omega (k)]=0$ for all $k$, it is possible for a system response to grow or damp algebraically as $h\approx{{t}^{s}}$ where $s$ is a fractional power. The growth is deduced through an asymptotic analysis of the Fourier integral that inherently invokes the superposition of an infinite number of modes. In this paper, the more typical case associated with the transition from stability to instability is examined in which Im$[\omega (k)]=0$ for a single mode (i.e. for one value of $k$) at neutral stability. Two partial differential equation systems are examined, one that has been constructed to elucidate key features of the stability threshold, and a second that models the well-studied problem of rectilinear Newtonian flow down an inclined plane. In both cases, algebraic growth/decay is deduced at the neutral stability boundary, and the propagation features of the responses are examined.

Numerical modelling of a dual-rotor marine current turbine in a rectilinear tidal flow

In this study, numerical simulation is used to investigate a counter-rotating dual-rotor marine current turbine (MCT) that is aligned for a rectilinear tidal current. Results of power and thrust coefficients and the mean axial velocity in the wake are compared with that of the blade element momentum (BEM) method coupled with the Park wake model. For a single-rotor MCT, small discrepancies are observed for front rotor, and larger discrepancies for rear rotor when comparing the CFD and BEM results. The mean axial velocity in the wake agrees better with the higher turbulence intensity (TI). CFD results shows that the power coefficient (CP) of rear rotor depends on the ambient turbulence intensity. The maximum CP of dual-rotor turbine is 5% higher than that of just the front rotor. Streamlines show that a large vortex is formed behind the rear rotor. The numerical simulations give more credibility to the BEM Park model, but also points to its sensitivity to the incoming turbulence intensity.

On the incipient formation of bars and channels on alluvial fans

AbstractThe morphodynamics of topographic expansion has been recently investigated both experimentally, by Sittoni et al., (2014) Shaw et al., (2018), and numerically Sittoni et al., 2014. Here, we study the basic mechanism that governs the evolution of topographic and expansions and explore the instability of the bottom topography under conditions of steady but spatially expanding flow. We model the expanding flow via a by configuration where water and sediments are supplied from a central hole and flow on a cone shaped surface confined by lateral walls. The governing equations are the shallow‐water equations coupled with the Exner equation, written in cylindrical coordinates. We initially approach the problem analytically by considering the conditions required for the basic state, consisting of a pure radial flow and bottom profile, to lose stability to small amplitude perturbations. This analysis suggests that more than one mode may be unstable, encouraging us to extend the analysis to the nonlinear regime. We do this through numerical modeling of the full governing equations, which allows us to predict the establishment of a bar pattern whose features are similar to those experimentally observed. Two prominent features of the finite‐amplitude bar pattern are (1) bar apices are distributed at a radial distance from the inflow consistent with work of Shaw et al. (2018); and (2) that the flow aspect ratio of the interbar areas remain high without provoking further instability. Both features imply that in general expansion acts to reduce bar development relative to an equivalent rectilinear flow. © 2019 John Wiley & Sons, Ltd.

Flow with heat transfer in a rotating cavity

An integral relation of the temperature spatial boundary layer energy equation, which allows integration over the surface of any shape to determine the thickness of the energy loss, was obtained. The equations for determining the energy loss of the temperature spatial boundary layer thickness are necessary to determine the local heat transfer coefficients for the characteristic cases of flow, taking heat exchange into account. The corresponding flows in the power unit cavities are considered. Turbulent flows of a gaseous flow were considered. Calculations for local heat transfer coefficients are defined. The local heat transfer coefficient for a rectilinear flow, a rotational flow according to the law of a solid, and a rotational flow according to the law of a free vortex were determined. Calculations for local heat transfer coefficients are defined as Stanton Criteria.

Dynamics and surface stability of a cylindrical cavitation bubble in a rectilinear vortex

In this paper, we formulate the dynamic equations of radial and surface modes for a cylindrical cavitation bubble subject to a prescribed uniform rectilinear vortex flow. The potential flow in the bulk volume of the external flow is modelled using the general mode decomposition approach. The stability of surface modes is investigated under linear analysis. The effects of confinement due to a limited flow domain in a water tunnel and viscosity at the bubble surface are evaluated, which can be fairly neglected for the cylindrical cavitation bubbles discussed. Our model is capable of predicting the developments of surface modes, which agrees well with experimental observations reported in the literature. We derive the Mathieu structure in the dynamic equation of the surface oscillation and the associated instability condition of the surface mode oscillations. The numerical results confirm that the Mathieu-type instability controls the stability diagrams and the emergence of surface modes under specific radial oscillation.

Surface Disentanglement and Slip in a Polymer Melt: A Molecular Dynamics Study

We perform nonequilibrium molecular dynamics shear flow simulations of an entangled polymer melt consisting of flexible linear chains. A steady-state rectilinear shear flow is imposed by sliding ex...

In-plane permeability distribution mapping of isotropic mats using flow front detection

In-plane permeability of textile fabrics is often characterized by one-dimensional rectilinear flow experiments, displaying limitations related to potential race-tracking effects and the need to run experiments at several fiber volume fractions. We propose a practical approach to alleviate these drawbacks. Resin flow front location is detected by image processing of videos and coupled to a Control Volume Finite Element solver with an error minimization routine based on Levenberg-Marquardt method comparing numerical and experimental fill times of all control volumes. Permeability of an isotropic random mat was characterized through reference experiments: cases with intentionally introduced race-tracking and cases with varying permeability along the resin flow direction with three different sections and fiber volume fractions. The method led to an efficient permeability determination and provided valuable insights on the statistics of spatial permeability distribution while highlighting the benefits of a thresholding algorithm for interpretation of permeability experiments in the presence of race-tracking.

Role of inertia and thixotropy in start-up flows of aging soft materials: Transient dynamics and shear banding in a rate-controlled flow field

We analyze the interplay between fluid inertia and thixotropy during the transient start-up dynamics of a fluidity model which captures the rheological behavior of aging soft (glassy) materials, in a rectilinear shear flow upon application of a step shear rate. We observe that when the steady-state flow curve is nonmonotonic, the system shows transient and/or apparent steady-state shear banding in close qualitative agreement with experimental observations. Due to competition between inhomogeneous aging and rejuvenation caused by fluid inertia during start up, we show that there is an apparent steady-state banding at large times (compared to the relevant momentum diffusion timescale) even for shear rates such that the steady state flow curve allows for a homogeneous flow. Thus, for aging soft glassy materials, the shear rate for achieving homogeneous flow is not necessarily given by the steady-state flow curve. We also observe that the transient and apparent steady-state shear banding behavior is not correlated to the negative slope of the stress-strain dependence during the transient. This work also emphasizes that in order to arrive at a realistic description of shear banding behavior in aging (thixotropic) soft materials, inertia may not always be neglected during the start-up dynamics.We analyze the interplay between fluid inertia and thixotropy during the transient start-up dynamics of a fluidity model which captures the rheological behavior of aging soft (glassy) materials, in a rectilinear shear flow upon application of a step shear rate. We observe that when the steady-state flow curve is nonmonotonic, the system shows transient and/or apparent steady-state shear banding in close qualitative agreement with experimental observations. Due to competition between inhomogeneous aging and rejuvenation caused by fluid inertia during start up, we show that there is an apparent steady-state banding at large times (compared to the relevant momentum diffusion timescale) even for shear rates such that the steady state flow curve allows for a homogeneous flow. Thus, for aging soft glassy materials, the shear rate for achieving homogeneous flow is not necessarily given by the steady-state flow curve. We also observe that the transient and apparent steady-state shear banding behavior is not corre...

Effect of graphic element type on visual perceptions of curvilinear and rectilinear flow diagrams

This study replicated a study conducted by Branch, Rezabek and Cochenour (1998) who contended that perception and interpretation can be influenced by the type of graphic elements used to compose a diagram. Because instructional design conditions resemble complex situations that require learning development systems sufficient to address the diversity and variety of actions required for the successful operation of intentional learning environments. The idea of matching the concomitant complexity of a process with the inherent complexity within a specific context is consistent with the law of requisite variety, which contends that in order to properly facilitate the quantity and diversity of a situation, you must have the ability to generate an equal quantity and diversity of responses. Instructional designers who utilize process models to generate teaching and learning materials will find the results of this study valuable as they consider effective ways to visualize flow diagrams intended to convey complex content. This study is relevant and important to the visual literacy as it seeks to answer the question: Do varieties of flow diagrams conveying similar content stimulate similar viewer perceptions? This study confirmed the results of the original 1998 study indicating that diagrams conveying similar flow patterns elicit similar adjectives.

An exploration and further study of an enhanced Oldroyd model

The Oldroyd 6-constant constitutive model for polymeric liquids [J. G. Oldroyd, “On the formulation of rheological equations of state,” Proc. R. Soc. A 200, 523 (1950)] was shown in the work of Bird [“A modification of the Oldroyd model for rigid dumbbell suspensions with Brownian motion,” Z. Angew. Math. Phys. 23, 157 (1972)] to have insufficient flexibility even to describe all second-order time-dependent behaviors of the simple molecular model of rigid dumbbells in solution. Bird proposed an enhancement of the Oldroyd model that would remove this deficiency. The advantage of such a continuum constitutive model is that it is far easier to use in solving specific flow problems than the more physical, but far more cumbersome, molecular models. Thus, if this enhanced constitutive model is indeed able to replicate the results of the molecular models, it should be extremely useful over the applicable range. Here, we employ the enhanced constitutive model of Bird [Z. Angew. Math. Phys. 23, 157 (1972)] to solve four different flow problems, and we verify that our solutions coincide exactly with those of a molecular model: through third order for rectilinear steady shear flow and steady extensional flow, and for one steady non-rectilinear flow (eccentric disk rheometer flow); and through second order for one unsteady (i.e., oscillatory) shear flow, thus providing strong confirmation of the physical veracity and utility of this continuum constitutive model, at least for small and moderate shear or extension rates.

Mixing and spreading of multiphase fluids in heterogeneous bimodal porous media

We investigate the impact of heterogeneous bimodal porous media on fluid mixing and spreading in viscously-unstable flows. Previous studies have mostly studied miscible mixing and spreading behavior in unimodal media. We characterize the temporal evolution of these processes in bimodal media and under both miscible and partially miscible conditions. We model advection-diffusion transport of a finite volume of $$\hbox {CO}_2$$ diluting within a rectilinear background flow of a multicomponent compressible hydrocarbon fluid. Accurate numerical simulations are performed to capture the details of hydrodynamic instabilities as well as the heterogeneity channelling. Thermodynamic phase behavior and Fickian diffusion are represented based on rigorous equation of state. We generate by means of a Markov Chain approach the permeability fields that represent facies architecture by volume fractions of each facies unit. Our results show that bimodal media significantly alter the flow pattern and spreading dynamics, especially at lower proportions of the high-permeability facies. However, we find the miscible mixing to be less sensitive to bimodal media, as a result of a delicate balance between fingering and permeability channeling. On other hand, spreading is usually lower in partially miscible flows, but this can be overridden by channeling due to bimodal media. The new hydrothermodynamic mechanisms that predominantly drive most of the mixing in partially miscible systems are still in effect even in bimodal media regardless of the facies architecture. Therefore, partially miscible mixing is negligibly impacted by bimodal heterogeneity. Our qualitative and quantitative results elucidate the key flow processes resulting from bimodal structures, and also rationalize the distinct mixing and spreading behaviors that emerge differently from the interplay between hydrothermodynamic mechanisms and flow channeling.

An experimental study of rivulet flow in low-boiling liquid driven by gas flow in a minichannel

Flow regimes in a low-boiling dielectric liquid driven by gas flow in a minichannel have been experimentally studied, and a map of regimes involving 11 varieties has been constructed. It is established that a rectilinear rivulet flow is observed in a restricted range of liquid and gas flow rates.

On the pulsating flow behavior of a biological fluid: human blood

In this work, the rectilinear flow of a complex fluid (human blood) under a pulsating time-dependent pressure gradient is analyzed. A first approximation of the real case of blood flowing in a vein is described. The normalized pressure gradient simulates the pumping work of the heart while the flow geometry (circular tube) is assumed rigid, smooth, and cylindrical. The rheological behavior of blood with different cholesterol levels is modeled using the Bautista–Manero–Puig (BMP) constitutive equation. According to the analytical solution, a flow enhancement is predicted to first order which represents the optimum pumping work of the heart which governs the flow of blood in the entire body. This work is a contribution to the understanding of the complex rheology involved in the discontinuous pressure-driven flow of blood in the human body.

A Kinetic Model for the Sedimentation of Rod--Like Particles

We consider a coupled system consisting of a kinetic equation coupled to a macroscopic Stokes (or Navier--Stokes) equation and describing the motion of a suspension of rigid rods in gravity. A reciprocal coupling leads to the formation of clusters: The buoyancy force creates a macroscopic velocity gradient that causes the microscopic particles to align so that their sedimentation reinforces the formation of clusters of higher particle density. We provide a quantitative analysis of cluster formation. We derive a nonlinear moment closure model, which consists of evolution equations for the density and second order moments and that uses the structure of spherical harmonics to suggest a closure strategy. For a rectilinear flow we employ the moment closure together with a quasi-dynamic approximation to derive an effective equation. The effective equation is an advection-diffusion equation with nonisotropic diffusion coupled to a Poisson equation, and belongs to the class of the so-called flux-limited Keller--Segel models. For shear flows, we provide an argument for the validity of the effective equation and perform numerical comparisons that indicate good agreement between the original system and the effective theory. For rectilinear flow we show numerical results which indicate that the quasi-dynamic provides accurate approximations. Finally, a linear stability analysis on the moment system shows that linear theory predicts a wavelength selection mechanism for the cluster width, provided that the Reynolds number is larger than zero.

Simultaneous pulsatile flow and oscillating wall of a non-Newtonian liquid

In this work, analytical predictions of the rectilinear flow of a non-Newtonian liquid are given. The fluid is subjected to a combined flow: A pulsatile time-dependent pressure gradient and a random longitudinal vibration at the wall acting simultaneously. The fluctuating component of the combined pressure gradient and oscillating flow is assumed to be of small amplitude and can be adequately represented by a weakly stochastic process, for which a quasi-static perturbation solution scheme is suggested, in terms of a small parameter. This flow is analyzed with the Tanner constitutive equation model with the viscosity function represented by the Ellis model. According to the coupled Tanner-Ellis model, the flow enhancement can be separated in two contributions (pulsatile and oscillating mechanisms) and the power requirement is always positive and can be interpreted as the sum of a pulsatile, oscillating, and the coupled systems respectively. Both expressions depend on the amplitude of the oscillations, the perturbation parameter, the exponent of the Ellis model (associated to the shear thinning or thickening mechanisms), and the Reynolds and Deborah numbers. At small wall stress values, the flow enhancement is dominated by the axial wall oscillations whereas at high wall stress values, the system is governed by the pulsating noise perturbation. The flow transition is obtained for a critical shear stress which is a function of the Reynolds number, dimensionless frequency and the ratio of the two amplitudes associated with the pulsating and oscillating perturbations. In addition, the flow enhancement is compared with analytical and numerical predictions of the Reiner-Phillipoff and Carreau models. Finally, the flow enhancement and power requirement are predicted using biological rheometric data of blood with low cholesterol content.

Characteristics and generation of elastic turbulence in a three-dimensional parallel plate channel using direct numerical simulation**Project supported by the National Natural Science Foundation of China (Grant Nos. 51276046 and 51506037), the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (Grant No. 51421063), the China Postdoctoral Science Foundation (Grant No. 2016M591526), the Heilongjiang Postdoctoral Fund, China

Direct numerical simulations (DNSs) of purely elastic turbulence in rectilinear shear flows in a three-dimensional (3D) parallel plate channel were carried out, by which numerical databases were established. Based on the numerical databases, the present paper analyzed the structural and statistical characteristics of the elastic turbulence including flow patterns, the wall effect on the turbulent kinetic energy spectrum, and the local relationship between the flow motion and the microstructures’ behavior. Moreover, to address the underlying physical mechanism of elastic turbulence, its generation was presented in terms of the global energy budget. The results showed that the flow structures in elastic turbulence were 3D with spatial scales on the order of the geometrical characteristic length, and vortex tubes were more likely to be embedded in the regions where the polymers were strongly stretched. In addition, the patterns of microstructures’ elongation behave like a filament. From the results of the turbulent kinetic energy budget, it was found that the continuous energy releasing from the polymers into the main flow was the main source of the generation and maintenance of the elastic turbulent status.

Mathematical Model for Isothermal Wire-Coating From a Bath of Giesekus Viscoelastic Fluid

A mathematical model of wire-coating based on Giesekus constitutive equation is analyzed under isothermal conditions. It is desired to see the functional dependence of Giesekus model parameters on the important operating variables in the wire-coating process, which include volumetric flow rate (later referred to as flow rate), shear stress at the wire surface (later referred to as shear stress), force required for pulling the wire (later referred to as force), and radius of the coated wire (later referred to as coated wire thickness). To this end, the equation governing the laminar, incompressible, and rectilinear flow is first derived and then solved analytically for the case of vanishing axial pressure gradient. A numerical procedure is described to obtain the solution for the case of nonvanishing pressure gradient. Our results indicate that the magnitude of shear stress and force follow a decreasing trend with increasing Giesekus model parameters in both cases. The flow rate and coated wire thickness decrease on increasing the Giesekus model parameters when there is no imposed pressure gradient. However, in the presence of pressure gradient these variables first decrease with increasing Giesekus model parameters and then follow an increasing trend.