Two-dimensional Channel Flow Research Articles

Forecasting two-dimensional channel flow using machine learning

Over the past decade, the integration of artificial neural networks (ANNs) has garnered significant interest, capitalizing on their ability to discern intricate patterns within data. Focused on enhancing computational efficiency, this article explores the application of ANNs in forecasting fluid-dynamics simulations, particularly for the benchmark problem of fluid flow in a two-dimensional (2D) channel. Leveraging a multilayer perceptron trained on finite volume method numerical data, for both interpolation and extrapolation estimations and various grid resolutions, our findings demonstrate the ANN's prowess as a swift and accurate surrogate for traditional numerical methods. Overall, the results of this work mark a pioneering step toward leveraging machine learning for modeling complex relationships in fluids phenomena, promising transformative advancements in computational fluid dynamics.

Quantum algorithm for solving the advection equation using Hamiltonian simulation

A quantum algorithm for solving the advection equation by embedding the discrete time-marching operator into Hamiltonian simulations is presented. One-dimensional advection can be simulated directly since the central finite-difference operator for first-order derivatives is anti-Hermitian. Here this is extended to industrially relevant multidimensional flows with realistic boundary conditions and arbitrary finite-difference stencils. A single copy of the initial quantum state is required and the circuit depth grows linearly with the required number of time steps, the sparsity of the time-marching operator, and the inverse of the allowable error. State-vector simulations of a scalar transported in a two-dimensional channel flow and lid-driven cavity configuration are presented as a proof of concept of the proposed approach. Published by the American Physical Society 2024

Enhanced heat transfer in a two-dimensional serpentine micro-channel using elastic polymers

Elastic turbulence has emerged as a promising method to enhance heat transfer performance at the microscale. However, previous studies have mainly focused on the overall convective heat transfer performance in curved channels, overlooking the fact that the chaotic flow intensity varies along the streamline, leading to diverse local heat transfer characteristics. In this study, we systematically investigate the hydraulic and thermal properties of a dilute polymer solution under elastic turbulence conditions, where the inflow conditions exhibit a vanishing Reynolds number (Re) and high Weissenberg number (Wi), enabling a comprehensive understanding of the influence of polymers on the system. Through extensive direct numerical simulations using Rheotool, a two-dimensional curvilinear channel flow of an Oldroyd-B viscoelastic fluid is analyzed. By examining the variations of the friction factor and Nusselt number along the serpentine channel, we unveil both global and local characteristics of elastic turbulence. Based on the Wi value, we identify three distinct regimes. In the first regime (0<Wi≤3), we observe approximately 10% heat transfer enhancement accompanied by a roughly 5% reduction in the friction factor compared to laminar flow, known as polymer-induced thermal conductivity enhancement. In the second regime (3<Wi≤5), we observe a steep linear increase in heat transfer (around 30%) at the expense of up to 15% enhanced friction factor. Finally, in the fully developed elastic turbulence regime (Wi>5), we observe a remarkable heat transfer enhancement of up to 60% along with a reduced friction factor. The significant enhancement of heat transfer with increasing Wi can be attributed to the intensifying elastic instability resulting from the balance between normal stresses and streamlined curvatures.

Heat and concentration analysis of two-layered muco-ciliary third grade fluid flow in human airways

Understanding the mechanisms involved in the movement and clearance of mucus within the human airways is important from a physiological perspective. A mathematical model of muco-ciliary two-layered fluid flow in a finite two-dimensional channel is proposed. Due to the presence of both the airway ciliary layer (ACL) and the periciliary liquid layer (PCL) in airways epithelial cells, the two-layered model is adopted. The third grade fluid models is used to characterize the viscoelastic nature of mucus secreted in the airways. The mathematical modeling of two-layer flow problem is simplified by using long wavelength and small Reynolds number approximation. A formulated set of partial differential equations (PDEs) is solved for series-form solutions of velocity, temperature, concentration, and pressure gradient by using the Adomian decomposition method (ADM). The analysis delineated that with an increase in pressure gradient at airways entrance ξ the velocity and temperature increases while concentration decreases. Deborah numbers impact ACL and PCL velocities differently, with De(A) influencing flow direction and De(P) causing fluid to flow faster in the forward direction. It also emphasizes the significance of the rate of thermal diffusion, viscous dissipation, and relaxation time. The results showed that the suggested two-layered muco-ciliary model provides a better description of mucus transport in the human airways. The pressure gradient at the airways entrance has a significant impact on mucus transport through the airways.

A pressure-loss model for flow-through round-hole perforated plates of moderate porosity and thickness in laminar and turbulent flow regimes

In this paper, we proposed a novel fluid flow model for pressure loss through plates with circular perforations in both laminar and turbulent flows. The design of this model is based on the recent measurements conducted at ONERA in the framework of the ongoing European Union H2020 INVENTOR project, as well as an existing model for laminar flows. The new model is then validated against existing numerical simulations in the laminar regime and experiments in the turbulent regime. Overall, the predictions given by the new model agree well with the numerical simulations and experiments, and are superior to other models in the literature. This is significant, considering that the present model is much simpler than these previous models. To demonstrate the applicability of the new model in numerical simulations, two-dimensional channel flows are simulated using Reynolds-averaged Navier–Stokes (RANS) equations with the new model as a pressure-drop source term added to the momentum equations. Results show that the RANS predictions agree very well with the present model predictions.

An invariance constrained deep learning network for partial differential equation discovery

The discovery of partial differential equations (PDEs) from datasets has attracted increased attention. However, the discovery of governing equations from sparse data with high noise is still very challenging due to the difficulty of derivatives computation and the disturbance of noise. Moreover, the selection principles for the candidate library to meet physical laws need to be further studied. The invariance is one of the fundamental laws for governing equations. In this study, we propose an invariance constrained deep learning network (ICNet) for the discovery of PDEs. Considering that temporal and spatial translation invariance (Galilean invariance) is a fundamental property of physical laws, we filter the candidates that cannot meet the requirement of the Galilean transformations. Subsequently, we embedded the fixed and possible terms into the loss function of neural network, significantly countering the effect of sparse data with high noise. Then, by filtering out redundant terms without fixing learnable parameters during the training process, the governing equations discovered by the ICNet method can effectively approximate the real governing equations. We select the one-dimensional (1D) Kuramoto–Sivashinsky equation, the two-dimensional (2D) Burgers equation, the equation of two-dimensional channel flow over an obstacle, and the equation of three-dimensional (3D) intracranial aneurysm as examples to verify the superiority of the ICNet for fluid mechanics. Furthermore, we extend similar invariance methods to the discovery of wave equation (Lorentz Invariance) and verify it through single and coupled Klein–Gordon equation. The results show that the ICNet method with physical constraints exhibits excellent performance in governing equations discovery from sparse and noisy data.

An analytical and comparative study of swallowing in a tumor-infected oesophagus: a mathematical model.

This study discusses non-steady effects encountered in peristaltic flows in oesophagus. The purpose of this communication is to evolve a mechanism to diagnose tumor in an oesophagus mathematically. The tumor is modelled by generic bump function of certain height and width. The method of solution follows long wavelength and low-Reynolds number approximations for unsteady flow, while integrations have been performed numerically in order to plot graphs, which reveal various characteristics of the flow. The goal is to assess how pressure varies across the tumor's width. The spatial, as well as temporal, dependence of pressure has been studied in the laboratory frame of reference. The pressure distribution for tumor-infected oesophagus is compared with that of normal oesophagus. An intensified pressure is obtained in the presence of tumor. The interruption while swallowing through benign oesophageal tumor is confirmed by an abrupt pressure rise across the tumor's width. Tumor position also plays a significant role whether it is at contraction or relaxation of walls. Additionally, wall-shear-stress, volumetric flow rate and streamlines have also been described and compared with that without tumor growth. The expressions corresponding to all the physical quantities are computed numerically. Further, this model may also be implemented to the two-dimensional channel flow for an industrial application.

Multistability of elasto-inertial two-dimensional channel flow

Elasto-inertial turbulence (EIT) is a recently discovered two-dimensional chaotic flow state observed in dilute polymer solutions. Two possibilities are currently hypothesized to be linked to the dynamical origins of EIT: (i) viscoelastic Tollmien–Schlichting waves and (ii) a centre-mode instability. The nonlinear evolution of the centre mode leads to a travelling wave with an ‘arrowhead’ structure in the polymer conformation, a structure also observed instantaneously in simulations of EIT. In this work we conduct a suite of two-dimensional direct numerical simulations spanning a wide range of polymeric flow parameters to examine the possible dynamical connection between the arrowhead and EIT. Our calculations reveal (up to) four coexistent attractors: the laminar state and a steady arrowhead regime (SAR), along with EIT and a ‘chaotic arrowhead regime’ (CAR). The SAR is stable for all parameters considered here, while the final pair of (chaotic) flow states are visually very similar and can be distinguished only by the presence of a weak polymer arrowhead structure in the CAR regime. Analysis of energy transfers between the flow and the polymer indicates that both chaotic regimes are maintained by an identical near-wall mechanism and that the weak arrowhead does not play a role. Our results suggest that the arrowhead is a benign flow structure that is disconnected from the self-sustaining mechanics of EIT.

Toward tuning flow charecteristics in microchannel by nanotechnology and electrokinetic: Numerical simulation of heterogenous electroosmotic flow

Nanotechnology in recent years helps researcehers to design flow rate and profile in microsized channel via making surface charge heterogenous. This paper numerically simulates the electroosmotic flow inside a microchannel with non-uniform Zeta potential (ZP). The problem is a two-dimensional, incompressible, steady, and laminar channel flow between two parallel plates. The numerical results show that the flow rate changes compared to a constant ZP by ascending, descending, and parabolic modifications of the wall ZP at the mid-length of the microchannel. Results show that flow volume rate increases by microchannel width from 4 mm3/s to 6.5 mm3/s in best condition.

A new model of time-dependent fractional second grade fluid for two-dimensional channel flow with heat transfer

The goal of the current paper is to create a novel model for the two-dimensional flow (TDF) of a second-grade fluid and the transfer of heat due to free convection. The second-grade fluid travels through the porous media and is electrically conducted. The governing equation for fluid velocity and temperature is formulated as a set of partial differential equations jointly. The model is developed in fractional form by applying the Caputo-Fabrizio (CF) fractional derivative approach. The two-dimensional flow problem is modeled in terms of one-sided coupled fractional partial differential equations with corresponding physical conditions imposed on the fluid flow and temperature. The problem is initially converted to a dimensionless form and then solved for the exact solutions by applying joint Fourier and Laplace transforms. Exact solutions are examined for fluid velocity and temperature and then in limiting cases are reduced to some well-known fluid motions. Some special cases are also obtained from the general solutions. For the numerical results, Mathcad-15 software is used and the results are plotted in various graphs. The temperature, and velocity profiles are discussed and highlighted for embedded flow parameters. The model obtained in this work is new and can be extended for other fluid models hence this article provides a base for future research.

Characteristic-Based Volume Penalization-Imposed Wall Function Method for Turbulent Boundary Layer Modeling

A method to approximate near-wall boundary conditions for the compressible Reynolds-Averaged Navier–Stokes equations is proposed. The differential formulation to match the external and the wall function solutions is reformulated in a form of the generalized characteristic-based volume penalization method to model the transfer of the shear stress from the outer region of the boundary layer to the wall. The exchange location is specified implicitly in terms of a localized source term in the boundary layer equation written as a function of the distance from the wall normalized by the viscous length scale. The shear stress on the wall is determined by solving an auxiliary equation for the wall-stress imposing the analytical wall function solution through the characteristic-based volume penalization method. The proposed method noticeably reduces the near-wall mesh resolution requirements without a significant modification of the numerical algorithm and completely eliminates the ill-defined explicit solution matching procedure. The developed approach is numerically implemented using the vertex-centered control volume method on structured meshes. Its effectiveness is demonstrated by solving two test problems: the two-dimensional channel flow and turbulent flow over an infinitely thin plate.

Nonlinear optimal perturbations and formation mechanism of localized wave packet in channel flow

The subcritical transition in a two-dimensional channel flow is characterized by the emergence of localized wave packet (LWP). In this paper, the nonlinear nonmodal optimization method is used, and when the target time is long enough the minimal seed, the minimal-energy perturbation triggering the transition is found to be the localized wave packet tilted upstream with energy scaling as Re−3.8 for Re&amp;gt;2500. The formation of LWP from a minimal seed includes three stages. First, the disturbance kinetic energy of the minimal seed increases to a local maximum through a transient growth governed by the Orr mechanism, and second, large scale vortex structures are generated due to the nonlinear forcing mainly contributed by the wave components and causes a streamwise symmetry breaking, i.e., a long but weak upstream tail and a strong downstream front are formed. As a result, the perturbation structure approaches the unstable lower branch solution and is attracted and captured at the last stage by the stable upper branch solution of LWP in the phase space.

Linear stability analysis of purely elastic travelling-wave solutions in pressure-driven channel flows

Recent studies of pressure-driven flows of dilute polymer solutions in straight channels demonstrated the existence of two-dimensional coherent structures that are disconnected from the laminar state and appear through a subcritical bifurcation from infinity. These travelling-wave solutions were suggested to organise the phase-space dynamics of purely elastic and elasto-inertial chaotic channel flows. Here, we consider a wide range of parameters, covering the purely elastic and elasto-inertial cases, and demonstrate that the two-dimensional travelling-wave solutions are unstable when embedded in sufficiently wide three-dimensional domains. Our work demonstrates that studies of purely elastic and elasto-inertial turbulence in straight channels require three-dimensional simulations, and no reliable conclusions can be drawn from studying strictly two-dimensional channel flows.

Slip boundary effect on the critical Reynolds number of subcritical transition in channel flow

In this letter, the effect of slip boundary on the origin of subcritical transition in two-dimensional channel flows is studied numerically and theoretically. It is shown that both the positive and the negative slip lengths will increase the critical Reynolds number of localized wave packet and hence postpone the transition. By applying a variable transformation and expanding the variables about a small slip length, it is illustrated that the slip boundary effect only exists in the second and higher order modulations of the no-slip solution, and hence explains the power law found in simulations, i.e. the relative increment of the critical Reynolds number due to the slip boundary is proportional to the square of the slip length.

On the Stability and Control of Two-Dimensional Channel Flow

Abstract A direct numerical simulation is used to solve the two-dimensional plane Poiseuille flow for three different stability cases; specifically, they are a supercritical case at a Reynolds number of 10,000, a critical-stable case at a Reynolds number of 5772.22, and subcritical case at a Reynolds number of 1000. The perturbations are developed using the eigenfunctions of Orr–Sommerfeld equation's solution. In many applications, the flow was required to be fully laminar. As a result, a model-based controller is developed for stabilizing the flow field using unsteady strong suction and blowing technique, through distributed slots on the two walls of the channel. This technique is introduced to cancel the propagating wave in the boundary-layers near the two walls. Promising results are achieved for the unstable and critical-stable cases. The stable case is tested. Slight improvements in its growth rate are recorded. In turn, a faster response for the flow field is achieved.

High-order pressure estimates for Navier-Stokes Runge-Kutta solvers using stage pseudo-pressures

This note addresses the question of whether stage pseudo-pressures can be used to build high-accuracy instantaneous pressure estimates in the context of projection-based Navier-Stokes solvers. The construction of such estimates using inter-stage pseudo-pressures is not straightforward, especially when time-dependent boundary conditions are present. New formulas are introduced that circumvent the limitation imposed by this type of boundary condition. While additional numerical costs might be involved in the construction of such estimates, the formulas are robust and show how one is able to recover high-order estimates of the pressure from within a Runge-Kutta pressure-projection scheme. The proposed formulas are then numerically tested on a two-dimensional channel flow simulation with unsteady inflow condition and show expected convergence rates.

Pattern preservation during the decay and growth of localized wave packet in two-dimensional channel flow

In this paper, the decay and growth of localized wave packet (LWP) in a two-dimensional plane-Poiseuille flow are studied numerically and theoretically. When the Reynolds number (Re) is less than a critical value Rec, the disturbance kinetic energy Ek of LWP decreases monotonically with time and experiences three decay periods, i.e., the initial and the final steep descent periods and the middle plateau period. Higher initial Ek of a decaying LWP corresponds to longer lifetime. According to the simulations, the lifetime scales as (Rec−Re)−1/2, indicating a divergence of lifetime as Re approaches Rec, a phenomenon known as “critical slowing-down.” By proposing a pattern preservation approximation, i.e., the integral kinematic properties (e.g., the disturbance enstrophy) of an evolving LWP are independent of Re and single valued functions of Ek, the disturbance kinetic energy equation can be transformed into the classical differential equation for saddle-node bifurcation, by which the lifetimes of decaying LWPs can be derived, supporting the −1/2 scaling law. Furthermore, by applying the pattern preservation approximation and the integral kinematic properties obtained as Re&amp;lt;Rec, the Reynolds number and the corresponding Ek of the whole lower branch, the turning point, and the upper-branch LWPs with Ek&amp;lt;0.15 are predicted successfully with the disturbance kinetic energy equation, indicating that the pattern preservation is an intrinsic feature of this localized transitional structure.

Population Balance Models for Particulate Flows in Porous Media: Breakage and Shear-Induced Events

Transport and particulate processes are ubiquitous in environmental, industrial and biological applications, often involving complex geometries and porous media. In this work we present a general population balance model for particle transport at the pore-scale, including aggregation, breakage and surface deposition. The various terms in the equations are analysed with a dimensional analysis, including a novel collision-induced breakage mechanism, and split into one- and two-particles processes. While the first are linear processes, they might both depend on local flow properties (e.g. shear). This means that the upscaling (via volume averaging and homogenisation) to a macroscopic (Darcy-scale) description requires closures assumptions. We discuss this problem and derive an effective macroscopic term for the shear-induced events, such as breakage caused by shear forces on the transported particles. We focus on breakage events as prototype for linear shear-induced events and derive upscaled breakage frequencies in periodic geometries, starting from nonlinear power-law dependence on the local fluid shear rate. Results are presented for a two-dimensional channel flow and a three dimensional regular arrangement of spheres, for arbitrarily fast (mixing-limited) events. Implications for linearised shear-induced collisions are also discussed. This work lays the foundations of a new general framework for multiscale modelling of particulate flows.

Cross-channel distribution and streamwise dispersion of micro-swimmers in a vertical channel flow: A study on the effects of shear, particle shape, and convective inertial torque

In quiescent water, gyrotactic micro-swimmers swim upward on average. This anti-gravity swimming behavior is usually thought to be caused by micro-swimmers' bottom-heaviness. However, recent research has shown the importance of convective inertial torque in the orientational dynamics of settling elongated particles, and the torque can cooperate with self-propulsion to result in an effective gyrotactic mechanism. In this paper, we compare the cross-channel distribution and streamwise dispersion of micro-swimmers with and without convective inertial torque in a two-dimensional vertical channel flow, using a recently proposed generalized Taylor dispersion method. Meanwhile, we incorporate other effects such as shear-shape interaction and wall accumulation. Reflective boundary condition and Robin boundary condition are imposed to represent periodic boundaries and mimic motility-induced wall accumulation effect, respectively. For non-gyrotactic inertialess elongated micro-swimmers, a transition from high-shear trapping regime to low-shear trapping regime appears, consistent with results in previous studies. For micro-swimmers with an effective gyrotaxis intensity resulting from the convective inertial torque, their macroscopic transport properties are essentially the same as those of inertialess micro-swimmers with the same aspect ratio and an equal physical gyrotaxis intensity. The non-monotonic variations of effective drift velocity and dispersivity as functions of the flow rate are also characterized. Additionally, upstream swimming behavior, which is reflected by negative drift velocity, is found in weak flows for both gyrotactic micro-swimmers and non-gyrotactic micro-swimmers with motility-induced wall accumulation.

Formation of Gel-Like Shear-Induced Structure with Dosing of Dilute Surfactant Solution and Its Effect on Turbulent Channel Flow

A shear-induced structure (SIS) is formed under appropriate concentration and shear conditions in a surfactant micellar solution. In this study, we performed experiments of surfactant solution dosing in a fully developed two-dimensional turbulent channel flow from a sintered metallic wire mesh plate attached to a side wall. We investigated the behavior of the solution under the elongation during its passing through the wire mesh and under the strong shear due to the channel flow. It was confirmed that the dosed solution containing a laser dye was visualized by a laser sheet, and the accumulated gel from the wire mesh formed a layer and developed with time. Consequently, on dosing the dilute surfactant solution from the wire mesh, a gel-like SIS layer was formed, which majorly covered the wire mesh plate. The gel-like SIS layer on the wire mesh plate acted as a sticky solid and restricted the flow in the channel. This layer continued to grow while dosing, owing to which the pressure drop of the channel flow significantly increased. The gel-like SIS layer grew rapidly even in the turbulent flow and reached the equilibrium thickness. After the termination of the dosing, the gel layer collapsed gradually. In addition, the thickness of the gel-like SIS layer (indicating the strength indirectly) strongly depended on the surfactant concentration and the elongation rate in the wire mesh.