Rigid Channel Research Articles

Acoustic streaming in a channel a moderate streaming Reynolds number

In this work, the generation of acoustic streaming in a rigid walled channel is examined. At low values of the streaming Reynolds number, the time-averaged fluid motion in the channel follows that given by Rayleigh. However, departure from the aforementioned result ensues as the magnitude of the streaming Reynolds number increases. Higher order nonlinear corrections to the Rayleigh streaming solution is given and are expressed in terms of a regular perturbation sequence in nondimensional particle amplitude. It is shown that the reduction in the amplitude of the axially directed streaming velocity is a function of the streaming Reynolds number.

A method to solve a problem of flow in a channel with two axisymmetric narrowings

A method is developed to solve a problem of flow in a flat rigid channel with two axisymmetric narrowings. The method has a second order of accuracy. In the method, the Navier-Stokes and discontinuity equations are solved by integrating over the elementary volumes (in which the integration domain is divided), spatial and temporal discretization of the obtained equations, as well as subsequent linearization of the discrete relationships and adjustment of the velocity and pressure fields. The temporal discretization is carried out on the basis of the implicit three-point asymmetric backward differencing scheme, whereas the spatial one is based on the TVD-scheme and the appropriate scheme of discretization of the temporal derivatives. An appropriate iterative method is applied to solve a system of linear algebraic equations.

Crustal Structure of Southwest China and Northern Vietnam From Ambient Noise Tomography: Implication for the Large‐Scale Material Transport Model in SE Tibet

AbstractSeveral models have been proposed to describe the tectonic evolution of SE Tibet and its marginal areas. Hence, high‐resolution crustal velocity models are essential to address this controversy. With waveform data from 73 broadband stations in southwest China and northern Vietnam, we invert for a 3‐D shear wave velocity model of the crust and uppermost mantle from ambient noise tomography. Our model reveals that the midlower crustal low‐velocity zone in the Xiaojiang Fault Zone extends farther southward across the Red River Fault to Vietnam and is approximately bounded by the Xiaojiang and Dien Bien Phu faults to the east. We suggest that the observed low‐velocity zone represents a mechanically weak zone in the mid‐lower crust, which may serve as a channel for efficient southward material transport in SE Tibet. With our results and previous evidence, we propose a combined model that integrates rigid block extrusion and crustal channel flow to describe the large‐scale material transport in SE Tibet. We further propose a two‐phase material transport model in SE Tibet after the India‐Eurasia plate collision: (1) rigid block extrusion between the right‐lateral Sagaing Fault and left‐lateral Red River Fault during the early Oligocene‐early Miocene and (2) a combined model of rigid block extrusion and material channel flow in the mid‐lower crust from the late Miocene to the present. The southward crustal material transport is likely to be diverted along two major channels around the more rigid crust beneath the inner zone of the Emeishan large igneous province.

A comparative study of longitudinal dispersion models in rigid vegetated compound meandering channels

Releasing and mixing of pollutants in rivers can cause serious threats for downstream users. Longitudinal dispersion is an important factor in describing pollutant transport process in rivers. The focus of this study is on the effect of floodplain rigid vegetation characteristics including its arrangement, density and relative depth (the ratio of the flow depth in the main channel to that over floodplain) on flow and longitudinal dispersion coefficient in a meandering channel with compound cross section. Digital image processing technique was used to measure the tracer concentration. Sequential images were continuously captured at seven sections downstream of release point. PVC cylinders were installed over the floodplain to simulate rigid vegetation in tandem and random arrangements. Acoustic Doppler Velocimeter (Micro-ADV) was used to measure 3-D velocity components. The results showed that roughening the flood plain with stems increases the longitudinal flow velocity and Reynolds shear stress in the main channel, while these parameters decrease in the flood plain compared to non-vegetated cases. As a result, in the presence of rigid vegetation, the travel time decreases in the main channel up to 20% compared to non-vegetated conditions. As the relative flow depth increases, the dimensionless longitudinal dispersion coefficient, K/U∗H, decreases up to 74%. Also, the dimensionless longitudinal dispersion coefficient increases up to 38% with stem density in a specific relative flow depth of Dr = 0.11. Finally, a comparison has been made between laboratory data and some well-known previously reported models. Later, the most accurate equations are presented for predicting the longitudinal dispersion coefficient in rigid vegetated compound meandering channels. The results of the present study reveal that rigid vegetation over flood plain can be used as an alternative method in river rehabilitation projects for environmental management purposes.

Tuning mechanical response in granular layers by adding rigid particle channel

The inhomogeneity of spatial packing by particles with different physical properties can significantly affect mechanical properties of granular packings. In this paper, a new approach by adding rigid particle channel is put forward to tune the mechanical response of granular layers induced by external loading. Based on the single-layer channel model, a phase diagram is firstly proposed to describe the crossover of mechanical response between a single-peaked and double-peaked feature, in which the tunable range of external loading and effective region of channel position are two key factors that reflect the tuning effect of this approach. Its tuning mechanism is further explored based on the variations of propagating feature of contact forces, and a linear function is proposed to predict the optimal position of the channel in systems with different sizes. Furthermore, the dependence of tuning effect on the spatial configuration and the number of rigid particle layers is also discussed in a double-layer and multi-layer rigid particle channel models, which can obviously improve the tunable effect but also undergo different tuning processes. By adding different rigid particle channels to actively change propagation paths of contact forces and weaken the anisotropy in vertical stress field within granular system, it has been verified that this approach is feasible to enhance the elasticity of whole system and tune its mechanical response.

Dual-Channel, Molecular-Sieving Core/Shell ZIF@MOF Architectures as Engineered Fillers in Hybrid Membranes for Highly Selective CO2 Separation.

A novel core/shell porous crystalline structure was prepared using a large pore metal organic framework (MOF, UiO-66-NH2, pore size, ∼ 0.6 nm) as core surrounded by a small pore zeolitic imidazolate framework (ZIF, ZIF-8, pore size, ∼ 0.4 nm) through a layer-by-layer deposition method and subsequently used as an engineered filler to construct hybrid polysulfone (PSF) membranes for CO2 capture. Compared to traditional fillers utilizing only one type of porous material with rigid channels (either large or small), our custom designed core/shell fillers possess clear advantages via pore engineering: the large internal channels of the UiO-66-NH2 MOFs create molecular highways to accelerate molecular transport through the membrane, while the thin shells with small pores (ZIF-8) or even smaller pores generated at the interface by the imperfect registry between the overlapping pores of ZIF and MOF enhance molecular sieving thus serving to distinguish slightly larger N2 molecules (kinetic diameter, 0.364 nm) from smaller CO2 molecules (kinetic diameter, 0.33 nm). The resultant core/shell ZIF@MOF and as-prepared hybrid PSF membranes were characterized by transmission electron microscopy, X-ray diffraction, wide-angle X-ray scattering, scanning electron microscopy, Fourier transform infrared, thermogravimetric analysis, differential scanning calorimetry, and contact angle tests. The dependence of the separation performance of the membranes on the MOF/ZIF ratio was also studied by varying the number of layers of ZIF coatings. The integrated PSF-ZIF@MOF hybrid membrane (40 wt % loading) with optimized ZIF coating cycles showed improved hydrophobicity and excellent CO2 separation performance by simultaneously increasing CO2 permeability (CO2 permeability of 45.2 barrer, 710% higher than PSF membrane) and CO2/N2 selectivity (CO2/N2 selectivity of 39, 50% higher than PSF membrane), which is superior to most reported hybrid PSF membranes. The strategy of using dual-channel molecular sieving core/shell porous crystals in hybrid membranes thus provides a promising means for CO2 capture from flue gas.

Experimental analysis of sediment incipient motion in rigid boundary open channels

Incipient motion of sediment is one of the main aspects of the sedimentation process. Determination of the minimum shear stress or velocity required to initiate the motion of sediment particles is a crucial task in the rigid boundary drainage system design. This study investigates incipient motion through laboratory experiments conducted in trapezoidal, rectangular, circular, U-shape and V-bottom cross-section smooth channels using four different size-sands. Experimental data are analyzed using the shear stress and velocity approaches. Shields method is used in the shear stress approach while formulation proposed by Novak and Nalluri is used as the velocity approach. New relationships are proposed for computing shear stress and velocity required for incipient motion in each of the channels. Results are compared with the corresponding models available in the literature. Data collected in this study are found in an acceptable agreement with the existing models. Channel cross-section shape plays an important role in incipient motion of sediment. Among the channels, the rectangular and V-bottom channels require the lowest and the highest shear stress and velocity for the initiation of sediment motion, respectively.

Solute dispersion by electroosmotic flow through soft microchannels

Abstract We study the hydrodynamic dispersion (HD) by electroosmotic flow in soft microchannels. Considering a fully developed flow in a slit microchannel of low surface potential and adopting the Taylor dispersion theory, we derive analytical solutions for the solute concentration field and the effective dispersion coefficient. We also conduct numerical analyses to broaden the paper’s scope to high surface potentials and to specify a criterion for the validity of the Debye-Huckel linearization in soft microconduits as well as to investigate the broadening of an analyte band from the time of injection. It is demonstrated that the effective dispersion coefficient of a neutral solute band is generally larger for thicker polyelectrolyte layers (PEL). This means that the hydrodynamic dispersion in electroosmotic flow usually increases by grafting a PEL to the surface. It is, however, possible to reduce the HD dispersion by appropriately altering the channel surface. Furthermore, it is found that higher PEL frictions lead to smaller HD. In addition, unlike rigid channels, a smaller HD is not necessarily achieved for a PEL-grafted microchannel by decreasing the surface potential. Finally, anomalies observed in the electrical potential and velocity distributions of soft microchannels are shown to be caused due to the creation of a triple-EDL within and outside the PEL.

A versatile plug microvalve for microfluidic applications

Most of the available microvalves include complicated fabrication steps and multiple materials. We present a microvalve which is inspired from macroplug valves. The plug microvalve is fabricated by boring a hole through a rigid cylindrical rod and inserting it through a microfluidic chip. It simply functions by rotating the rod which aligns or misaligns the valve port with the microchannel. The rod is made up of a rigid material for applying the valve to an elastic polydimethylsiloxane (PDMS) microchannel. The valve can also be used for a rigid channel by inserting the rod into an elastic tubing. Therefore, the presented microvalve can be used for both elastomeric and thermoplastic channels. The plug microvalve can be applied to a prefabricated microchannel and does not require modification of the mold design. We have verified the repeatability and robustness of the valve by repetitive operation cycles using a servo motor. The plug microvalve is adaptable to numerous microfluidic applications. We have shown three modes of operation for the microvalve including fluid flow control across multiple intersecting channels. Integrating the microvalve to some commonly used microfluidic designs, we demonstrated the versatility and the practicality of the microvalve for controlling flow focusing, microdroplet sorting and rapid chemical agent detection. This low-cost microvalve significantly minimizes the prototyping time for microfluidic systems.

Velocity-based analysis of sediment incipient deposition in rigid boundary open channels.

Drainage systems must be designed in a way to minimize undesired problems such as decrease in hydraulic capacity of the channel, blockage and transport of pollutants due to deposition of sediment. Channel design considering self-cleansing criteria are used to solve the sedimentation problem. Incipient deposition is one of the non-deposition self-cleansing design criteria that can be used as a conservative method for channel design. Experimental studies have been carried out in five different cross-section channels, namely trapezoidal, rectangular, circular, U-shape and V-bottom. Experiments were performed in a tilting flume using four different sizes of sands as sediment in nine different channel bed slopes. Two well-known methods, namely the Novak & Nalluri and Yang methods are considered for the analysis of sediment motion. Equations developed using experimental data are found to be in agreement with the literature. It is concluded that the design velocity depends on the shape of the channel cross-section. Rectangular and V-bottom channels need lower and higher incipient deposition velocities, respectively, in comparison with other channels.

Open thin-layer cascade reactors for saline microalgae production evaluated in a physically simulated Mediterranean summer climate

While microalgae hold the promise for conversion of sunlight and CO2 to a wide variety of products, the economics of algae processes are still debatable. We have designed an open thin-layer cascade photobioreactor for high-cell density cultivation of saline microalgae to advance economic microalgae mass production. Pilot-scale reactors with a surface area of up to 8m2 (cultivation volume 50–140L) were constructed and evaluated using a dynamic climate simulation technology (light, air temperature and humidity) integrating natural sunlight and multi-color LED arrays for a highly realistic reproduction of the sunlight spectrum. Batch processes with Nannochloropsis salina were performed in these reactors in the physically simulated Mediterranean summer climate of Almería, Spain – an ideal location for outdoor microalgae cultivation. Two reactor variants were examined: one with a smooth but expensive rigid channel made of polyethylene sheets, and one with a more uneven but significantly less expensive channel made of pond liner. Maximal intra-day growth rates of 1.9d−1 were observed at a cell density of 1–3gL−1. The maximal cell density of 50gL−1 was obtained within 25days. These high growth rates and cell densities markedly exceed literature data. No difference in growth between the channel variants was observed. This suggests that cost-efficient large-scale thin-layer cascade reactors with inexpensive pond liner channels are feasible. The high cell density allows a reduction of harvesting cost. Optimal process conditions were identified by analyzing the batch and daily economic bioprocess metrics: At a cell density of 17gL−1, an areal biomass productivity of 25gm−2d−1 (volumetric productivity 4gL−1d−1) and a photosynthetic conversion efficiency of 4.6% were observed. The reactor design is discussed in detail to encourage further advancement of thin-layer algal cultivation technology.

Development of group method of data handling based on genetic algorithm to predict incipient motion in rigid rectangular storm water channel

Sediment transport is a revalent vital process in fluvial and coastal environments, and incipient motion is an issue inseparably bound to this topic. This study utilizes a novel hybrid method based on Group Method of Data Handling (GMDH) and Genetic Algorithm (GA) to design GMDH structural (GMDH-GA). Also, SingularValue Decomposition (SVD) was utilized to compute the linear coecient vectors. In order to predict the densimetric Froude number (Fr), the ratio of median diameter of particle size to hydraulic radius (d=R) and the ratio of sediment deposit thickness to hydraulic radius (ts=R) are utilized as e ective parameters. Using three diff erent sources of experimental data and GMDH-GA model, a new equation is proposed to predict incipient motion. The performance of development equation is compared using GMDH-GA and traditional equations . The results indicate that the presented equation is more accurate (RMSE = 0:18 and MAPE = 6:48%) than traditional methods. Also, a sensitivity analysis is presented to study the performance of each input combination in predicting incipient motion.

Asymptotic stability and transient growth in pulsatile Poiseuille flow through a compliant channel

The time-asymptotic linear stability of pulsatile flow in a channel with compliant walls is studied together with the evaluation of modal transient growth within the pulsation period of the basic flow as well as non-modal transient growth. Both one (vertical-displacement) and two (vertical and axial) degrees-of-freedom compliant-wall models are implemented. Two approaches are developed to study the dynamics of the coupled fluid–structure system, the first being a Floquet analysis in which disturbances are decomposed into a product of exponential growth and a sum of harmonics, while the second is a time-stepping technique for the evolution of the fundamental solution (monodromy) matrix. A parametric study of stability in the non-dimensional parameter space, principally defined by Reynolds number ($Re$), Womersley number ($Wo$) and amplitude of the applied pressure modulation ($\unicode[STIX]{x1D6EC}$), is then conducted for compliant walls of fixed geometric and material properties. The flow through a rigid channel is shown to be destabilized by pulsation for low $Wo$, stabilized due to Stokes-layer effects at intermediate $Wo$, while the critical $Re$ approaches the steady Poiseuille-flow result at high $Wo$, and that these effects are made more pronounced by increasing $\unicode[STIX]{x1D6EC}$. Wall flexibility is shown to be stabilizing throughout the $Wo$ range but, for the relatively stiff wall used, is more effective at high $Wo$. Axial displacements are shown to have negligible effect on the results based upon only vertical deformation of the compliant wall. The effect of structural damping in the compliant-wall dynamics is destabilizing, thereby suggesting that the dominant inflectional (Rayleigh) instability is of the Class A (negative-energy) type. It is shown that very high levels of modal transient growth can occur at low $Wo$, and this mechanism could therefore be more important than asymptotic amplification in causing transition to turbulent flow for two-dimensional disturbances. Wall flexibility is shown to ameliorate mildly this phenomenon. As $Wo$ is increased, modal transient growth becomes progressively less important and the non-modal mechanism can cause similar levels of transient growth. We also show that oblique waves having non-zero transverse wavenumbers are stable to higher values of critical $Re$ than their two-dimensional counterparts. Finally, we identify an additional instability branch at high $Re$ that corresponds to wall-based travelling-wave flutter. We show that this is stabilized by the inclusion of structural damping, thereby confirming that it is of the Class B (positive-energy) instability type.

Reopening modes of a collapsed elasto-rigid channel

Motivated by the reopening mechanics of strongly collapsed airways, we study the steady propagation of an air finger through a collapsed oil-filled channel with a single compliant wall. In a previous study using fully compliant elastic tubes, a ‘pointed’ air finger was found to propagate at high speed and low pressure, which, if clinically accessible, offers the potential for rapid reopening of highly collapsed airways with minimal tissue damage (Heap & Juel Phys. Fluids, vol. 20 (8), 2008, 081702). The mechanism underlying the selection of that pointed finger, however, remained unexplained. In this paper, we identify the required selection mechanism by conducting an experimental study in a simpler geometry: a rigid rectangular Hele-Shaw channel with an elastic top boundary. The constitutive behaviour of this elasto-rigid channel is nonlinear and broadly similar to that of an elastic tube, but unlike the tube, the channel’s cross-section adopts self-similar shapes from the undeformed state to the point of first near wall contact. The ensuing simplification of the vessel geometry enables the systematic investigation of the reopening dynamics in terms of increasing initial collapse. We find that for low levels of initial collapse, a single centred symmetric finger propagates in the channel and its shape is set by the tip curvature. As the level of collapse increases, the channel cross-section develops a central region of near opposite wall contact, and the finger shape evolves smoothly towards a ‘flat-tipped’ finger whose geometry is set by the strong depth gradient near the channel walls. We show that the flat-tipped mode of reopening is analogous to the pointed finger observed in tubes. Its propagation is sustained by the vessel’s extreme cross-sectional profile at high collapse, while vessel compliance is necessary to stabilise it. A simple scaling argument based on the dissipated power reveals that this reopening mode is preferred at higher propagation speeds when it becomes favourable to displace the elastic channel wall rather than the viscous fluid.

Статичний прогин пружних підстав жорсткого прямокутного каналу з рідиною.

In a linear formulation, the functions of static deflections of elastic bases in the form of fixed rectangular plates in a rigid rectangular channel with a two-layer ideal incompressible fluid separated by an elastic plate are obtained. The cases of plate degeneracy into membranes and the absence of one of the liquids are considered. Investigations of static deflections of plates from elastic and mass characteristics, densities and filling depths of liquids are conducted. On the basis of numerous studies, areas of change of dimensionless parameters are determined. With these parameters, the static problem is described within the framework of a linear theory. This is a prerequisite for solving a dynamic task.

Shape-adaptable hyperlens for acoustic magnifying imaging

Previous prototypes of acoustic hyperlens consist of rigid channels, which are unable to adapt in shape to the object under detection. We propose to overcome this limitation by employing soft plastic tubes that could guide acoustics with robustness against bending deformation. Based on the idea of soft-tube acoustics, acoustic magnifying hyperlens with planar input and output surfaces has been fabricated and validated experimentally. The shape-adaption capability of the soft-tube hyperlens is demonstrated by a controlled experiment, in which the magnifying super-resolution images remain stable when the lens input surface is curved. Our study suggests a feasible route toward constructing the flexible channel-structured acoustic metamaterials with the shape-adaption capability, opening then an additional degree of freedom for full control of sound.

Artificial neural network and regression models for flow velocity at sediment incipient deposition

A set of experiments for the determination of flow characteristics at sediment incipient deposition has been carried out in a trapezoidal cross-section channel. Using experimental data, a regression model is developed for computing velocity of flow in a trapezoidal cross-section channel at the incipient deposition condition and is presented together with already available regression models of rectangular, circular, and U-shape channels. A generalized regression model is also provided by combining the available data of any cross-section. For comparison of the models, a powerful tool, the artificial neural network (ANN) is used for modelling incipient deposition of sediment in rigid boundary channels. Three different ANN techniques, namely, the feed-forward back propagation (FFBP), generalized regression (GR), and radial basis function (RBF), are applied using six input variables; flow discharge, flow depth, channel bed slope, hydraulic radius, relative specific mass of sediment and median size of sediment particles; all taken from laboratory experiments. Hydrodynamic forces acting on sediment particles in the flow are considered in the regression models indirectly for deriving particle Froude number and relative particle size, both being dimensionless. The accuracy of the models is studied by the root mean square error (RMSE), the mean absolute percentage error (MAPE), the discrepancy ratio (Dr) and the concordance coefficient (CC). Evaluation of the models finds ANN models superior and some regression models with an acceptable performance. Therefore, it is concluded that appropriately constructed ANN and regression models can be developed and used for the rigid boundary channel design.

Fully localized solitary waves for the forced Kadomtsev–Petviashvili equation

The Kadomtsev–Petviashvili (KP) equation is a generalized form of the Korteweg–de Vries equation for a three-dimensional channel flow. Three-dimensional fully localized solitary wave solutions can be obtained when the effect of surface tension is significant; we refer to this as the KP-I equation. An exact solution of a three-dimensional fully localized stationary solution for the KP-I equation has been found in the absence of any obstacle on the rigid channel bottom. However, three-dimensional fully localized stationary solutions for the KP-I equation have not been found in the presence of a forcing neither analytically nor numerically. This forcing term comes from some obstacles in the rigid channel bottom. In this work, we focus on the fully localized solitary wave solutions when a positive bump or a negative hole is given as the rigid bottom configuration. The forced KP-I equation is defined in an infinite domain and it is reduced to a finite computational domain by introducing artificial boundary conditions. Interestingly, there are at least two distinct stationary lump-type solutions for a positive bump, while there are at least three distinct stationary lump-type solutions for a negative hole. Furthermore, we investigate their numerical stability by solving the forced time-dependent KP-I equation using them as initial conditions. Our numerical results confirm that there exists a stable stationary lump-type solitary wave solution for both a positive bump and a negative hole when they evolve in time.

Design of a new hybrid artificial neural network method based on decision trees for calculating the Froude number in rigid rectangular channels

Abstract A vital topic regarding the optimum and economical design of rigid boundary open channels such as sewers and drainage systems is determining the movement of sediment particles. In this study, the incipient motion of sediment is estimated using three datasets from literature, including a wide range of hydraulic parameters. Because existing equations do not consider the effect of sediment bed thickness on incipient motion estimation, this parameter is applied in this study along with the multilayer perceptron (MLP), a hybrid method based on decision trees (DT) (MLP-DT), to estimate incipient motion. According to a comparison with the observed experimental outcome, the proposed method performs well (MARE = 0.048, RMSE = 0.134, SI = 0.06, BIAS = -0.036). The performance of MLP and MLP-DT is compared with that of existing regression-based equations, and significantly higher performance over existing models is observed. Finally, an explicit expression for practical engineering is also provided.

On the Yih–Marangoni instability of a two-phase plane Poiseuille flow in a hydrophobic channel

The linear stability analysis of a plane Poiseuille flow of two immiscible, incompressible fluids of different viscosities and densities in a hydrophobic channel, in the presence of an insoluble surfactant at the interface is examined, within the framework of Orr–Sommerfeld system. The walls of the channel are modeled as walls with velocity slip/no-slip. The equations governing the flow system are solved numerically by a Chebyshev collocation method for a wide range of dimensionless parameters describing the flow system. The effects of slip on the neutral stability boundaries for the interface modes in the presence/absence of an insoluble surfactant at the interface are examined for different thickness ratios of the two layers, with density and/or viscosity stratification. Slip conditions at the wall show a promise for control of the Yih–Marangoni instability of the corresponding flow system in a rigid channel. The influence of the parameters on the critical Reynolds number for the shear mode is assessed. The study reveals that it is possible to control instabilities in interface dominated rigid channel flows by designing the walls of the channel as hydrophobic/rough/porous or undulated surfaces as these can be modeled as one with slip at the substrates.