Incompressible Viscous Flow Research Articles

Extraction of Lagrangian Coherent Structures in the framework of the Lagrangian–Eulerian Stabilized Collocation Method (LESCM)

In recent years, the investigations on Lagrangian Coherent Structures (LCS) in complex flows have attracted increasing attention due to their ability to accurately describe flow field details. In this study, we propose a novel and accurate numerical technique based on the Lagrangian–Eulerian Stabilized Collocation Method (LESCM) for computing the Finite Time Lyapunov Exponents (FTLEs), which is essential for extracting LCSs in viscous incompressible flows. LESCM, previously employed for simulating fluid–structure interaction problems, was developed based on the Material Point Method (MPM). The hybrid Lagrangian–Eulerian​ description in LESCM enables explicit tracking of fluid flow trajectories throughout the simulation and direct evaluation of the FTLE field. Furthermore. The errors in FTLEs caused by the Particle Shifting Technique (PST) are completely avoided due to the Eulerian characteristic of LESCM as the deformation gradient is calculated based on fixed Eulerian nodes rather than fluid particles with unphysical shifting. Consequently, the novel technique based on LESCM surpasses the accuracy of pure Lagrangian particle methods and provides an accurate way of detecting complex LCSs in flow fields. Additionally, By harnessing the remarkable efficiency of LESCM, MATLAB can now handle up to 16 million particles with ease, eliminating the need for parallel computation techniques. Several numerical examples, such as 2D Taylor-Green​ vortices, flow passing a circular cylinder and a 3-dimensional shear driven cavity problem, have been tested to demonstrate the effectiveness of this novel approach under various conditions.

On a Navier–Stokes–Cahn–Hilliard system for viscous incompressible two-phase flows with chemotaxis, active transport and reaction

On a Navier–Stokes–Cahn–Hilliard system for viscous incompressible two-phase flows with chemotaxis, active transport and reaction

Novel computational fluid dynamics-finite element analysis solution for the study of flexible material wave energy converters

The use of flexible materials for primary mover and power takeoff of wave energy converters (WECs) has attracted considerable attention in recent years, owing to their potential to enhance the reliability, survivability, and wave energy conversion efficiency. Although some reduced order models have been used to study the fluid–structure interaction (FSI) responses of flexible wave energy converters (fWECs), they are somehow inappropriate due to their limited accuracy and applicability span. To gain a deeper understanding of the physical mechanisms in fWECs, a high-fidelity approach is required. In this work, we build up a fluid–structure interaction analysis framework based on computational fluid dynamics and a finite element analysis method. The incompressible viscous flow is resolved by solving three-dimensional unsteady Navier–Stokes equations with a finite volume approach. The structure dynamics are solved by a finite element method, taking the nonlinear behavior of flexible material into consideration. A strong coupling strategy is utilized to enhance the numerical stability and convergence of the iterative process. We demonstrate the present FSI tool is able to provide rich flow field information and structural response details, such as the velocity, pressure, and structural stress distribution. This is illustrated through several case studies, including two types of fWECs. The unsteady wave–structure-interaction and the associated nonlinear phenomena are also accurately captured by this tool.

On buoyancy‐driven viscous incompressible flows with various types of boundary conditions

AbstractIn this paper, we study the existence and uniqueness of solutions to the initial‐boundary‐value problem for time‐dependent flows of heat‐conducting incompressible fluids through the two‐dimensional channel. The boundary conditions are of two types: the so‐called “do nothing” boundary condition on the outflow and the so‐called Navier boundary conditions on the solid walls of the channel. A priori estimates play a crucial role in existential analysis, however, the considered mixed boundary conditions do not enable us to derive an energy‐type estimate of the solution. Our aim is to prove the existence and uniqueness of a solution on a sufficiently short time interval for arbitrarily large data.

A mass-preserving level set method for simulating 2D/3D fluid flows with deformed interface

This research paper focuses on the development of a novel interface-capturing solver for predicting two-phase flow in 2D/3D Cartesian meshes within the framework of Eulerian approaches. The primary objective is to ensure mass conservation and accurate capture of interface topology. To achieve this, a mass-preserving level set advection equation formulated as a scalar sign-distance function is proposed. The key innovation of the Eulerian solver lies in the incorporation of a scalar speed function for robust reconstruction of the classical level set equation. The effectiveness and reliability of the proposed flow solver in solving incompressible two-phase viscous flow equations are demonstrated through several benchmark problems.

Numerical study of transient convective turbulent boundary layer flow along a vertical plate: analysis of kinetic energy and its dissipation rate

ABSTRACT The present article numerically investigates the turbulent buoyancy-driven (natural convection) flow along a vertical plate with a low Reynolds turbulence two-equation k-ϵ model. The deployed turbulence model is appropriate for low Reynolds number (LRN) turbulent flow adjacent to a solid boundary, and the turbulence kinetic energy (TKE) and dissipation rate of TKE are estimated using the momentum equations and are solved simultaneously with the mean flow conservation equations. Two-dimensional time-dependent viscous incompressible turbulent flow is simulated. This flow domain is governed by a highly non-linear group of partial differential equations, namely the time-averaged continuity, momentum, and energy, and also the flow property is determined through TKE, and dissipation rate of TKE equations. Since these equations are not solvable using analytical methods, an implicit second-order finite difference method is employed to solve the governing turbulent flow equations numerically. The simulated time-averaged velocity, temperature, TKE, and dissipation rate of TKE profiles along with friction factor and heat transfer rate are computed for different values of turbulent Reynolds and Prandtl numbers. Average velocity, temperature, turbulence energy, and dissipation rate under both transient and steady-state conditions are decreased with increment in . There is a decrement in average transient velocity and turbulence energy rates with increasing values, whereas the average temperature profile increases. Average steady temperature and turbulence energy profiles are also enhanced with rising values of . The majority of researchers focus on laminar flow and thus far turbulent flow has mainly been addressed through experiments only. To better elucidate the flow in this condition, the novelty of the present study is to utilize a numerical FDM procedure to probe more deeply into the turbulence characteristics in buoyancy-driven (natural convection) flow along a vertical plate with a low Reynolds turbulence two-equation k-ϵ model, as this topic is fundamental to many applications in science and engineering. Furthermore, the results of the turbulent flow simulations obtained from the current model are corroborated with existing results for the special case of laminar flow and a good correlation is achieved.

Unsteady Carbon Nanotubes Nanofluid Flow due to a Moving Cylinder with Thermal Radiation and Temperature Oscillation Effects

This paper discusses transient two-dimensional boundary layer laminar viscous incompressible free convective flow of nanofluids containing carbon nanotubes (SWCNTs and MWCNTs) over a moving vertical cylinder in the presence of thermal radiation and temperature oscillation. The governing boundary layer equations are converted to a dimensionless form and then solved using the Crank Nicolson type’s unconditionally stable and convergent implicit finite difference method. With diverse parameters such as Grashof number (Gr), volume fraction (Φ), phase angle (ωt), and thermal radiation parameter (N), numerical results are achieved for velocity and temperature profiles along with Nusselt number and skin friction coefficients. The numerical results are analysed in detail using graphs for both water-based nanofluid and kerosene-based nanofluids with single and multi-wall carbon nanotubes as the nanomaterials. It has been found that CNTs Water-based nanofluid has higher temperatures, velocities, skin friction coefficient values for all Gr, N, Φ, and ωt when compared to kerosene-based nanofluid with CNTs. But, Kerosene-based CNTs nanofluid has a higher Nusselt number coefficient values concerning all Gr, N, Φ, and ωt than water-based CNTs nanofluid.

The Role of Double-Tentacled Cooperative Kinematics on the Hydrodynamics of a Self-propelled Swimmer

In this study, we proposed an underwater robotic swimmer integrating dual-actuated composite tentacles. We employed overlapping grid technology to manipulate virtual swimmers and performed simulations of incompressible viscous flow. To facilitate the distinction between three driving modes (the reverse, homologous, and interlace modes), the rear flexible module of the swimmer was divided into three components: thigh links, calf links, and caudal fins. The cooperative motion mechanism behind the double-tentacled module exhibited special hydrodynamic properties. Under the same kinematic parameters, the reverse mode exhibited the best energy-saving and propulsion effect, whereas the homologous mode was affected by lateral energy loss, thus resulting in the worst propulsion effect. However, the joint system exhibited anti-interference and spanwise flexibility. The interlace mode produced a certain error in the lateral displacement, and the propulsion efficiency was between the former two modes. Compared with traditional fish-like robots, the diverse actuation morphologies of the swimmer reported in this study exhibit extremely powerful self-propelled functionality, and its key features, including the geometry of an aquatic squid and the kinematics of the stretched body-caudal fin pattern, offer insights into the analysis of self-propelled hydrodynamics.

Physics-informed neural network based on a new adaptive gradient descent algorithm for solving partial differential equations of flow problems

Physics-informed neural network (PINN) is an emerging technique for solving partial differential equations (PDEs) of flow problems. Due to the advantage of low computational cost, the gradient descent algorithms coupled with the weighted objectives method are usually used to optimize loss functions in the PINN training. However, the interaction mechanisms between gradients of loss functions are not fully clarified, leading to poor performances in loss functions optimization. For this, an adaptive gradient descent algorithm (AGDA) is proposed based on the interaction mechanisms analyses and then validated by analytical PDEs and flow problems. First, the interaction mechanisms of loss functions gradients in the PINN training based on the traditional Adam optimizer are analyzed. The main factors responsible for the poor performances of the Adam optimizer are identified. Then, a new AGDA optimizer is developed for the PINN training by two modifications: (1) balancing the magnitude difference of loss functions gradients and (2) eliminating the gradient directions conflict. Finally, three types of PDEs (elliptic, hyperbolic, and parabolic) and four viscous incompressible flow problems are selected to validate the proposed algorithm. It is found that to reach the specified accuracy, the required training time of the AGDA optimizer is about 16%–90% of the Adam optimizer and 41%–64% of the PCGrad optimizer, and the demanded number of iterations is about 10%–68% of the Adam optimizer and 38%–77% of the PCGrad optimizer. Therefore, the PINN method coupled with the AGDA optimizer is a more efficient and robust technique for solving partial differential equations of flow problems.

The heat transfer effects of MHD slip flow with suction and injection and radiation over a shrinking sheet by optimal homotopy analysis method

The current study investigates the laminar flow of boundary layer using a porous surface shrinking exponentially under varying magnetic field, suction/injection, radiation on velocity and thermal slips. The dimensionless nonlinear differential equations were also defined in terms of governing partial differential equations and applying similarity transformations. The equations were analytically solved following the homotopy analysis method (HAM). An excellent agreement is observed in comparison with theavailable literature in special case (Skin friction coefficient). In the current study, an analytic solution is obtained for the laminar incompressible MHD boundary layer viscous fluid flow problem on the exponentially electrically conducting porous shrinking surface. The impact of different parameters like injection/suction, Prandtl number, radiation, velocity slip, thermal slip, as well as the magnetic field on different velocity and temperature values have been presented graphically, and have been discussed in detail. The f″(0) skin friction rises with higher suction parameter s(>0) values, magnetic parameter M but it decreases when the slip parameter value is increased. Whereas heat transfer rate −θ′(0) rises with an increasing M, s and λ..

Lie derivatives of fundamental surface quantities in incompressible viscous flows

Lie derivative is an important concept in differential geometry. From the perspective of theoretical fluid dynamics, the present paper evaluates and interprets the Lie derivatives of the fundamental surface physical quantities (including skin friction, surface vorticity, and surface pressure) with respect to a characteristic velocity field in near-wall incompressible viscous flows. It is found that the Lie derivatives are directly associated with the boundary enstrophy flux, an orthogonal pair of skin friction and surface vorticity, and an orthogonal pair of surface enstrophy gradient and its conjugate vector, while components of the Lie derivatives in skin-friction-surface-vorticity orthogonal frame are related to four on-wall coupling scalar quantities (associated with the skin friction divergence and the surface vorticity divergence). The derived theoretical results are first evaluated in a laminar oblique Hiemenz flow and a turbulent channel flow. Then, features of the Lie derivatives are explored in a typical skin friction structure generated by a complex separated flow over a hill model. The present exposition provides a unique perspective of the Lie derivatives to the boundary vorticity dynamics and near-wall flow physics.

A Waveguide Model of the Developed Turbulent Boundary Layer

A study of the developed turbulent boundary layer that emerges when incompressible viscous fluid flows around a plate at a zero angle of attack and with zero longitudinal pressure gradient is presented. The waveguide approach is used for describing the turbulent boundary layer; in this approach, turbulent fluctuations are related with Tollmien–Schlichting waves that are in three-wave resonance. To study the original nonlinear system of equations, an estimate of hydrodynamic quantities is proposed that does not violate the generally accepted approach in the boundary layer but leads to the appearance of a new small parameter—the ratio of the thickness of the boundary layer momentum loss to the damping length of the least damped mode of the Tollmien–Schlichting waves. Equations for the coherent and stochastic parts of fluctuations are obtained on the basis of the method of multiple scales. The dispersion characteristics of waves of the least damped mode on the profile of the average longitudinal velocity of the developed turbulent boundary layer are determined, and the conditions for the multiple three-wave resonance of this mode of the Tollmien–Schlichting waves are analyzed. For the coherent part of the fluctuations, the fluctuation characteristics are compared with the known numerical results.

Efficiency of local Vanka smoother geometric multigrid preconditioning for space‐time finite element methods to the Navier–Stokes equations

AbstractNumerical simulation of incompressible viscous flow continues to remain a challenging task, in particular if three space dimensions are involved. Space‐time finite element methods feature the natural construction of higher order discretization schemes. They offer the potential to achieve accurate results on computationally feasible grids. Using a temporal test basis supported on the subintervals and linearizing the resulting algebraic problems by Newton's method yield linear systems of equations with block matrices built of (k + 1) × (k + 1) saddle point systems, where k denotes the polynomial order of the variational time discretization. We demonstrate numerically the efficiency of preconditioning GMRES iterations for solving these linear systems by a V‐cycle geometric multigrid approach based on a local Vanka smoother. The studies are done for the two‐ and three‐dimensional benchmark problem of flow around a cylinder. The robustness of the solver with respect to the piecewise polynomial orderkin time is analyzed and confirmed numerically.

On Shadowing Effects in the Flow around the Group of Circular Cylinders in the Geotechnical Applications

The purpose of the presented study is to investigate the influence of the distance between three infinite circular cylinders in a tandem group on their aerodynamic coefficients and the general flow pattern. The questions of the numerical simulation of viscous incompressible flow around a group of cylinders in the tandem arrangement are considered. The numerical study of the flow around the group of cylinders is based on unsteady Reynolds-averaged Navier-Stokes equations. The results are presented as a visualization of the instantaneous flow parameters and the dependencies of the averaged drag coefficients on the distance between the cylinders. Following the previous investigations, the flow parameters were chosen in a little-studied range, corresponding to the Reynolds number of 120 for a standalone cylinder. The distances between the centers of neighboring cylinders ranged from 1.1 to 6.0 cylinder diameters. Three characteristic flow patterns are distinguished depending on the distance between the cylinders. The first one is a steady-state flow similar to the flow around the standalone cylinder. This flow pattern is formed when the distance between the cylinders is less than three diameters. Increasing the distance between the centers up to four diameters produces the second flow pattern. The vortex street is formed behind the group while the flow between the cylinders remains steady. Further increasing the distance between the cylinders causes the formation of the third pattern when the flow between the cylinders becomes unsteady as well. The averaged drag coefficients for each cylinder in the group are obtained. The presented work helps better to understand the flow structure around the group of cylinders and can be used at the design stage in various engineering applications, including cooling towers, heat exchanger tubes, chimney stacks, marine platforms, and high-rise buildings.

Physics-Informed Neural Network for Flow Prediction Based on Flow Visualization in Bridge Engineering

Wind loads can endanger the safety and stability of bridges, especially long-span cable-supported bridges. Therefore, it is important to evaluate the potential wind loads during the bridge design stage. Traditionally, wind load evaluation is performed by wind tunnel testing, which is relatively expensive. With the development of computational fluid dynamics and high-performance computing, numerical simulations are becoming more accessible for designers. However, the costs required for accurate numerical results are still high, especially for high-fidelity simulations. Under this condition, searching for a more efficient method to evaluate the wind loads in bridge wind engineering has become a new goal. It seems that flow visualization is a good entry point. Although flow visualization techniques have been developed in recent years, it remains difficult to extract velocity and pressure fields from images. To address this problem, physics-informed neural networks (PINNs) have been developed and validated. This study establishes a PINN to investigate the two-dimensional viscous incompressible fluid flow passing a generic bridge deck section. Two cases with different Reynolds numbers are tested. After careful training, it is found that the PINN can accurately extract the velocity and pressure fields from the concentration field and predict the drag and lift coefficients. The results demonstrate that PINNs are a promising method for extracting useful flow information from flow visualization data in engineering applications.

Exact relations between Laplacian of near-wall scalar fields and surface quantities in incompressible viscous flow

In this short paper, we derive the on-wall values and the wall-normal derivatives of the Laplacians of pressure and kinetic energy density at the wall for incompressible viscous flow past a stationary wall. The theoretical results reveal some interesting on-wall coupling pairs that are composed of the fundamental surface physical quantities (including skin friction, surface vorticity and surface pressure) and surface curvature. The exact results are valid for flow past any stationary curved wall, which are valuable for understanding the near-wall viscous flow very close to the wall.

Unsteady Magnetohydrodynamic (MHD) Cu–Al2O3/Water Hybrid Nanofluid Flow and Heat Transfer from an Exponentially Accelerated Plate

The present study intends to explore heat transfer characteristics of the unsteady natural convective flow of Cu–Al2O3/water hybrid nanofluid due to exponentially accelerated vertical plate. 2D Laminar viscous incompressible boundary layer fluid flow is considered in the presence of MHD and accelerating parameter. The governing partial differential equations with appropriate boundary conditions are solved using the Crank-Nicolson numerical technique. Plots for skin friction coefficient, velocity, temperature, Nusselt number concerning Magnetic parameter (M), Accelerating parameter (a), Grashof number (Gr), Volume fraction (Φ2), and time are disclosed. The study imparted that Cu–Al2O3 hybrid nanoparticles with water as base fluid facilitate a higher heat transfer rate and soaring Nusselt number compared to nanofluid Cu/water. Furthermore, we found an elevated skin friction coefficient in nanofluid Cu/water than in hybrid nanofluid Cu–Al2O3/water in all non-dimensional parameters.

HYDRODYNAMIC STABILITY OF SWIRLING FLOWS WITH AXIAL RECIRCULATION ZONES

The problem of the motion of a viscous incompressible swirling flow in an axisymmetric channel has been numerically investigated. Various flow regimes have been obtained, including those with the formation of the axial recirculation zones. In the framework of linear theory, the stability of the obtained calculated flows with respect to non-axisymmetric perturbations is investigated on the assumption of local parallelism. The growth rates and phase velocities of unstable disturbances are calculated. In the presence of a reverse flow zone, the disturbances growth rates are increased significantly.

The novelty of using the AGM and FEM for solutions of partial differential and ordinary equations along a stretchable straight cylinder

Near the suction/injection area, a scientific definition for laminar boundary layer flow and heat transfer of an incompressible viscous flow over a stretching cylinder is given. In the study, differential equations with partial derivatives are converted into dimensionless coupled equations using numerical and analytical methods of Akbari- Ganji and Finite Elements Methods. The goal of this first stage of research and research on this topic is to use simplified forms to simplify equations using derivatives of simplified forms; the analysis of the displacement of the heat flux and the velocity gradient will be done using the changes of the Prandtl number. Based on the results obtained on this issue, it is found that the suction process increments surface firmness and quality, whereas the injection decreases surface skin friction. Also, at the points where the water and oil are attached to the surface of the cylinder, the heat has reached its maximum value, and as the distance increases along the Y axis, the temperature decreases. The highest temperature gradient is observed for water fluid. This shows that the use of water fluid around the cylinder accelerates the process of heat transfer from the surface to the outside of the boundary layer. One of the differences between the use of oil and water fluid around the cylinder according to the 2D contours is the difference in the temperature gradient of the two fluids. So that the highest temperature gradient is observed for water fluid.

Lamb dilatation and its hydrodynamic viscous flux in near-wall incompressible flows

In this paper, we introduce a new physical concept referred to as the wall-normal Lamb dilatation flux (WNLDF), which is defined as the wall-normal derivative of the Lamb dilatation (namely, the divergence of the Lamb vector) multiplied by the dynamic viscosity for incompressible viscous flows. It is proved that the boundary Lamb dilatation flux (BLDF, namely the wall-normal Lamb dilatation flux at the wall) is determined by the boundary enstrophy flux (BEF) and the surface curvature-induced contribution. As the first step to explore this new concept, the present study only considers flow past a stationary no-slip flat wall without curvature-fluid dynamic coupling effects. It is found that the temporal–spatial evolution rate of the WNLDF is contributed by four source terms, which can be explicitly expressed by using the fundamental surface quantities including skin friction (or surface vorticity) and surface pressure. Therefore, the instantaneous near-wall flow structures are directly related to the WNLDF in both laminar and turbulent flows. As an example, for the turbulent channel flow at Reτ=180, the intensification of the temporal–spatial evolution rate of the WNLDF is caused by the strong wall-normal velocity event (SWNVE) associated with quasi-streamwise vortices and high intermittency of the viscous sublayer. In addition, near the SWNVE, this evolution rate is mainly contributed by the dot product of skin friction and surface enstrophy gradient, as well as the coupling between the skin friction divergence and the boundary enstrophy. The exact results presented in this paper could provide new physical insights into complex near-wall flows.