Plane Channel Research Articles

Supersonic Gas Flow in a Plane Channel with a Normal Glow Discharge in the Magnetic Field

Supersonic Gas Flow in a Plane Channel with a Normal Glow Discharge in the Magnetic Field

Data-Guided Low-Reynolds-Number Corrections for Two-Equation Models

Abstract The baseline Launder–Spalding k−ε model cannot be integrated to the wall. This paper seeks to incorporate the entire law of the wall into the model while preserving the original k−ε framework structure. Our approach involves modifying the unclosed dissipation terms in the k and ε equations specifically within the wall layer according to direct numerical simulation (DNS) data. The resulting model effectively captures the mean flow characteristics in both the buffer layer and the logarithmic layer, resulting in robust predictions of skin friction for zero-pressure-gradient (ZPG) flat-plate boundary layers and plane channels. To further validate our formulation, we apply our model to boundary layers under varying pressure gradients, channels experiencing sudden deceleration, and flow over periodic hills, with highly favorable results. Although not the focus of this study, the methodology here applies equally to the k–ω formulation and yields improved predictions of the mean flow in the viscous sublayer and buffer layer.

Failure of a detonation wave in a plane channel with multiple obstacles

The results of numerical study of the interaction of a formed cellular detonation wave propagating in a plane channel occupied by a quiescent stoichiometric hydrogen-air mixture with multiple obstacles (barriers) located on the inner surface of the channel are given. The study is carried out to determine the conditions that ensure suppression of detonation. The influence of geometric parameters of the area with obstacles on wave propagation is studied. It is found that localization of the obstacles in a recess in the channel wall leads to a decrease in their destructive effect on detonation. Quenching of detonation combustion by the layer of a non-reacting gas located along the channel wall, limited by single barriers, is considered. The effect of gas composition on the interaction of the detonation wave with the layer is studied. Non-reacting gas mixtures, which, being filled into the area with obstacles, enhance the destructive effect of barriers on the detonation wave are proposed.

On the Correct Nusselt Numbers for Laminar Fully Developed Flow in a Plane Channel with Isothermal Walls

In all common heat transfer books, the Nusselt number ( Nu ) given for laminar fully developed incompressible flow in a plane channel with isothermal walls is Nu = 7.54 . This result is obtained through the neglect of viscous dissipation. However, we show that when the viscous dissipation is very small but not identically zero (which is a physical impossibility), the Nusselt number should be either Nu = 35 / 2 for a liquid or Nu = 0 for an ideal gas. Furthermore, the exact corresponding temperature distributions and mean temperatures for arbitrary viscous dissipation are given.

Numerical simulation of detonation propagation and extinction in two-phase gas-droplet ammonia fuel

Numerical simulations of detonation propagation and extinction in ammonia droplet-laden premixed ammonia–oxygen gas are performed in a 2-D planar channel. The sustained propagation and ultimate quenching of detonation with perturbations from ammonia droplets are observed under lower and larger values of initial droplet number density (Nd,0) and diameter (d0), respectively. The detonation always quenches under d0=15μm. The detonation propagation/extinction behaviour and cell structure are dependent on both d0 and Nd,0. The positive correlations between droplet volume fraction, inter-phase mass, momentum, and energy transfers and d0 are more nonlinear than their counterparts of Nd,0. The post-Mach stem region experiences higher-intensity detonative combustion and thus droplet evaporative, accelerative, and heating effects than the post-incident wave region. During the detonation extinction process, the detonation wave degenerates into detonative spots which then decouple into shock and reaction fronts; gaseous pressure, heat release rate, and nitric oxide volume fraction peaks decline.

Learning-Based Block-Wise Planar Channel Estimation for Time-Varying MIMO OFDM

Learning-Based Block-Wise Planar Channel Estimation for Time-Varying MIMO OFDM

Mechanisms and Morphological Time Scales of Avulsed Channel Process on the Modern Yellow River Delta

AbstractThe modern Yellow River Delta (YRD) has witnessed frequent channel avulsions followed by the morphological processes of “wandering‐ short‐lived braiding ‐merging” in history. However, process‐based investigation and relevant physics behind these processes remain poorly constrained. The present study complements the understanding for this evolution through numerical experiments. This is achieved by applying a two‐dimensional (2‐D) depth‐averaged fully coupled morphodynamic model that considers the feedbacks of sediment‐laden flow and bed deformation to a schematized fan‐shaped YRD. Under an uneven bed of uniform sediment, the avulsed processes of “wandering‐ short‐lived braiding ‐merging” during new channel routing on the YRD are satisfactorily reproduced by the present modelling in terms of the time evolution of planar channel pattern and channel length. Moreover, the mechanisms of the avulsed evolution have been elucidated through factor analysis on delta slope, incoming flow‐sediment conditions and artificial trenching, etc. It is suggested that morphological stability could be reached when a single meandering channel is finally sustained, of which the time scale is 4–8 years echoing the documented data of abandoned channels on the YRD. In addition, quantitative criteria have been advocated to help distinguishing the sub‐stages of the avulsed evolution together with the characteristic pattern judgement. Based on the above, implications for the YRD management are discussed.

Equilibrium Configurations of a Symmetric Body Immersed in a Stationary Navier–Stokes Flow in a Planar Channel

Equilibrium Configurations of a Symmetric Body Immersed in a Stationary Navier–Stokes Flow in a Planar Channel

ELECTRO-OSMOTIC EFFECT ON PERISTALTIC FLOW OF PHAN–THIEN–TANNER FLUID IN A PLANAR CHANNEL

Abstract There are several factors that can cause the excessive accumulation of biofluid in human tissue, such as pregnancy, local traumas, allergic responses or the use of certain therapeutic medications. This study aims to further investigate the shear-dependent peristaltic flow of Phan–Thien–Tanner (PTT) fluid within a planar channel by incorporating the phenomenon of electro-osmosis. This research is driven by the potential biomedical applications of this knowledge. The non-Newtonian fluid features of the PTT fluid model are considered as physiological fluid in a symmetric planar channel. This study is significant, as it demonstrates that the chyme in the small intestine can be modelled as a PTT fluid. The governing equations for the flow of the ionic liquid, thermal radiation and heat transfer, along with the Poisson–Boltzmann equation within the electrical double layer, are discussed. The long-wavelength ( $\delta \ll 1$ ) and low-Reynolds-number approximations ( $Re \to 0$ ) are used to simplify the simultaneous equations. The solutions analyse the Debye electronic length parameter, Helmholtz–Smoluchowski velocity, Prandtl number and thermal radiation. Additionally, streamlines are used to examine the phenomenon of entrapment. Graphs are used to explain the influence of different parameters on the flow and temperature. The findings of the current model have practical implications in the design of microfluidic devices for different particle transport phenomena at the micro level. Additionally, the noteworthy results highlight the advantages of electro-osmosis in controlling both flow and heat transfer. Ultimately, our objective is to use these findings as a guide for the advancement of lab-on-a-chip systems.

Geometrically parametrised reduced order models for studying the hysteresis of the Coanda effect in finite element-based incompressible fluid dynamics

This article presents a general reduced order model (ROM) framework for addressing fluid dynamics problems involving time-dependent geometric parametrisations. The framework integrates Proper Orthogonal Decomposition (POD) and Empirical Cubature Method (ECM) hyper-reduction techniques to effectively approximate incompressible computational fluid dynamics simulations. To demonstrate the applicability of this framework, we investigate the behaviour of a planar contraction-expansion channel geometry exhibiting bifurcating solutions known as the Coanda effect. By introducing time-dependent deformations to the channel geometry, we observe hysteresis phenomena in the solution.The paper provides a detailed formulation of the framework, including the stabilised finite elements full order model (FOM) and ROM, with a particular focus on the considerations related to geometric parametrisation. Subsequently, we present the results obtained from the simulations, analysing the solution behaviour in a phase space for the fluid velocity at a probe point, considered as the Quantity of Interest (QoI). Through qualitative and quantitative evaluations of the ROMs and hyper-reduced order models (HROMs), we demonstrate their ability to accurately reproduce the complete solution field and the QoI.While HROMs offer significant computational speedup, enabling efficient simulations, they do exhibit some errors, particularly for testing trajectories. However, their value lies in applications where the detection of the Coanda effect holds paramount importance, even if the selected bifurcation branch is incorrect. Alternatively, for more precise results, HROMs with lower speedups can be employed.

On the corrugation effect on thermo-fluids characteristics and entropy generation in channels equipped with wavy and straight sections

A numerical simulation was performed to investigate the characteristics of thermo-fluids and the irreversibility generation of laminar forced convection through three different channel designs. This article first presents a comprehensive study of combination of straight and wavy sections in order to create a balance between improved thermal performance from the wavy design and optimized flow properties from the straight section, leading to an overall enhancement in cooling efficiency. A novel design has been considered using a channel configuration that consists of different lengths of wavy and straight sections and is named (cases I, II, and III). The outcomes are shown in terms of average Nu, enhancement ratio (ER), performance factor, total irreversibility generation, as well as the contours of streamlines, isothermal, and Bejan numbers for different values of the Reynolds number range of 5≤Re≤400 and dimensionless wave amplitude 0.3≤α≤0.6. The results were compared of the three cases with the plane channel, revealing an augmentation in HTR of 73.7%, 64.9%, and 43.3% for cases III, II, and I, respectively. On the other hand, with both Re and α, the total irreversibility generation increases continuously.

Large eddy simulation of a turbulent channel flow using dynamic Smagorinsky subgrid scale model and differential equation wall model

A large eddy simulation (LES) is conducted in a plane channel flow which is turbulent. For understanding the mechanism of the turbulent motion more efficiently, the present study is an attempt to conduct the LES using a Dynamic Smagorinsky Model (DSM) and a Differential Equation Wall Model (DEWM). DSM is a subgrid-scale model and DEWM is for approximating the near wall layer. The simulation is performed in a domain of 2 π δ × 2 δ × π δwhich is discretized by 32 × 20 × 32grid points where δ is the channel half width. The discretization techniques have been used in the simulation, are the 3rd order low storage R-K method in time and 2nd order finite difference formulation in space. To assess the performance of the LES with DSM and DEWM, the simulation results are compared with direct numerical simulation (DNS) data and LES data using Standard Smagorinsky Model (SSM). Comparing the results in the essential turbulence statistical field it has been found that DSM performs better than SSM in most of the cases and shows better agreement with the DNS results. Flow structures in the turbulent flow field are compared in isosurfaces and contour plots, and found that tube-like vortical structures are randomly distributed over the entire flow field, and the number of the vortical structures are more for the DSM case than that of SSM.

Viscoplastic flows in channels with small aspect ratio: Bingham versus regularised models

We investigate the two-dimensional flows of a viscoplastic fluid in symmetric channels with impermeable walls under no-slip boundary conditions. To characterise the mechanical response of the viscoplastic fluid we consider both the celebrated Bingham model and a very general class of its regularisations. In order to make the problem amenable to analysis, we assume that the aspect ratio of the channel is small so that the lubrication approximation can be used. This allows us to obtain analytical solutions, perform an asymptotic analysis of the regularised solutions and compare the results predicted by the Bingham model and its regularisations. We find that in the limit as the regularisation parameter tends to zero, the regularised flow tends to those predicted by the Bingham model only in plane channels. In channels with curved walls, the results are instead markedly different.

Mathematical modeling of velocity field induced by the vortex

In new technological applications, it is important to use vortex distributions in the area for obtaining large velocity fields. This paper, it was calculated the distribution of the velocity field and distribution of stream function for ideal incompressible fluid, induced by a different system of the finite number of vortex threads: 1) circular vortex lines in a finite cylinder, positioned on its inner, 2) spiral vortex threads, positioned on the inner surface of the finite cylinder or cone, and 3) linear vortex lines in the plane channel, positioned on its boundary. An original method was used to calculate the components of the velocity vectors. Such kind of procedure allows calculating the velocity fields inside the domain depending on the arrangement, the intensity, and the radii of vortex lines. In this paper, we have developed a mathematical model for the process in the element of Hurricane Energy Transformer. This element is a central figure in the so-called RKA (ReaktionsKraftAnlage) used on the cars’ roofs.

Magneto-Permeability Effect in Ferrofluid Flow Through Porous Media Studied via Multiparticle Collision Dynamics

AbstractAs more and more promising applications of magnetic nanoparticles in complicated environments are explored, their flow properties in porous media are of increasing interest. We here propose a hybrid approach based on the multiparticle collision dynamics method extended to porous media via friction forces and coupled with Brownian dynamics simulations of the rotational motion of magnetic nanoparticles’ magnetic moment. We simulate flow in planar channels homogeneously filled with a porous medium and verify our implementation by reproducing the analytical velocity profile of the Darcy–Brinkman model in the non-magnetic case. In the presence of an externally applied magnetic field, the non-equilibrium magnetization and friction forces lead to field-dependent velocity profiles that result in effective, field-dependent permeabilities. We provide a theoretical expression for this magneto-permeability effect in analogy with the magneto-viscous effect. Finally, we study the flow through planar channels, where only the walls are covered with a porous medium. We find a smooth crossover from the Poiseuille profile in the center of the channel to Brinkman–Darcy flow in the porous layers. We propose a simple estimate of the thickness of the porous layer based on the flow rate and maximum flow velocity.

Failure of a Detonation Wave in a Plane Channel with Multiple Obstacles

Failure of a Detonation Wave in a Plane Channel with Multiple Obstacles

Стационарное протекание несжимаемой вязкой жидкости сквозь двухмерный разветвленный канал

The results of a numerical experiment for the problem of an incompressible viscous fluid stationary flow through a branched planar (two-dimensional) channel are presented. The region in which the flow occurs simulates either blood vessels or a river delta. The finite element method and a modification of the penalty method, as well as the splitting method, are used for calculations. The implementation of the calculation algorithm is using with the help the package FreeFem++. The main goal, in addition, of course, to study the properties and structure of the stationary flow, is to demonstrate the effectiveness of the proposed modification of the penalty method. It is assumed that the region has one input boundary section through which the liquid flows into the region, and several (five) boundary sections through which the liquid flows out of the region. The remaining sections of the region boundary are considered impermeable to liquid. The boundary condition corresponding to the Poiseuille flow in a plane rectilinear channel is set at the input section. Three types of boundary conditions are considered on the output boundary secctions. 1. The boundary conditions correspond to the conditions of conservation of motion of luid particles i. e. the material derivative of the velocity is zero. 2. The boundary conditions correspond to the setting of the flow velocity. 3. The boundary conditions correspond to the setting of the same pressure. The stationary solution is constructed by the relaxation method. In fact, a non-stationary problem is solved over a sufficiently large time interval. As an initial condition for a non-stationary problem, a flow is chosen that is a Poiseuille flow in some region near the input boundary. The dependence of the convergence rate of the relaxation method on the initial data is investigated. It is found that the Poiseuille flow, given at the input section of the boundary of the region, induces similar Poiseuille flows at the output boundaries sections of the region in all these cases of boundary conditions. For a region with five sections of the output boundaries for some configuration of the region, the presence of stationary vortex flows (‘maelstorm’) is found.

Revisiting Tensor Basis Neural Network for Reynolds stress modeling: Application to plane channel and square duct flows

Recent advances in computing power devoted to Computational Fluid Dynamics (CFD) have opened up a new avenue for addressing the turbulence closure problem through Machine Learning (ML). Several Tensor Basis Neural Network (TBNN) frameworks aimed at enhancing turbulence Reynolds-Averaged Navier–Stokes (RANS) modeling have recently been proposed in the literature as data-driven constitutive models for systems with known invariance properties. However, persistent ambiguities remain regarding the physical adequacy of applying the General Eddy Viscosity Model (GEVM) within these frameworks. This work aims at investigating this aspect in an a priori stage for better predictions of the Reynolds stress anisotropy tensor, while preserving the Galilean and rotational invariances. In particular, we propose a general framework providing optimal tensor basis models for two types of canonical flows with increasing complexity: Plane Channel Flow (PCF) and Square Duct Flow (SDF). Subsequently, deep neural networks based on these optimal models are trained using state-of-the-art strategies to achieve a balanced and physically sound prediction of the full anisotropy tensor. A priori results obtained by the proposed framework are in very good agreement with the reference Direct Numerical Simulations (DNS) data. Notably, our shallow network with three layers excels in providing accurate predictions of the anisotropy tensor for PCF at unobserved friction Reynolds numbers, both in interpolation and extrapolation scenarios. The learning of the SDF case is more challenging because of its physical nature but also due to a lack of training data at various regimes. We propose a numerical strategy to alleviate this problem based on Transfer Learning (TL). In order to more efficiently generalize to an unseen intermediate Reτ regime, we take advantage of our prior knowledge acquired from a training with a larger and wider dataset. Our results indicate the potential of the developed network model, and demonstrate the feasibility and efficiency of the TL process in terms of training data size and training time. Based on these results, we believe there is a promising future by integrating these neural networks into an adapted in-house RANS solver.

Density and confinement effects on fluid velocity slip

Understanding the velocity slip of fluids in channels of molecular length scales is essential for accurately manipulating their flow in engineering applications, such as in water desalination or, by reversing the process, osmotic power generation. This study addresses two major open questions, namely (a) the range of validity of the Navier-Stokes equations with slip boundary conditions in describing fluid flows within channels of molecular confinement, and (b) the effect of fluid density and confinement as well as surface properties, such as microscopic roughness and curvature, on fluid slippage along walls. Using a hard-sphere fluid model and describing the fluid-wall interactions by the Maxwell scattering kernel, an event-driven molecular dynamics simulation study was performed in planar and cylindrical channels of different sizes and accommodation coefficients with varying fluid densities. The results show that the well-known criterion for the slip solution, which is valid in rarefied conditions, also holds for a dense gas, i.e., the predictive accuracy improves with decreasing Knudsen numbers, as long as the channel size is larger than about ten molecular diameters. We also find that the key quantity influencing the friction coefficient of a fluid is the peak density at the walls, rather than the nominal density, the fluid confinement, or the channel curvature, as found in previous studies. In particular, higher nominal densities lead to higher density peaks, and therefore a decrease in slip, while tighter confinements lead to lower density peaks, and therefore an increase in slip, regardless of channel geometry. Furthermore, the velocity slip depends on the microscopic roughness via the Smoluchowski factor. These findings are a stepping stone towards a deeper understanding of the molecular mechanisms underlying fluid velocity slip in molecular-scale channels. Published by the American Physical Society 2024

Planar nanoscale vacuum channel transistors based on resistive switching

Resistance switching (RS) offers promising applications in a variety of areas. In particular, silicon oxide (SiO x ) under RS can serve as electron sources in new types of miniature vacuum electron tubes. In this work, planar nanoscale vacuum channel transistors (NVCTs) with graphene electrodes and RS SiO x electron sources were developed. In each RS-NVCT, the resistance between the ground and the gate underwent high–low–high transitions, which resulted from formation and subsequent rupture of Si conducting filaments. Electrons were emitted from the post-reset Si filaments and the current received by the collector (I C) was well controlled by the gate voltage (V G). The transfer characteristics reveal that I C was quite sensitive to V G when RS occurred. With V G sweeping from 0 to −20 V, the obtained subthreshold swing (SS) of 76 mV dec−1 was quite close to the theoretical limit of the SS of a field effect transistor at room temperature (60 mV dec−1). The largest ON/OFF ratio was of the order of 106. The output characteristics of the devices indicate that the dependence of I C on the collector voltage (V C) weakened at high V C values. These results demonstrate the application potential of RS-NVCTs as either switching devices or amplifiers.