Incompressible Viscous Flow Research Articles

Numerical solutions for magneto-convective boundary layer slip flow from a nonlinear stretching sheet with wall transpiration and thermal radiation effects

A mathematical model is presented for magnetohydrodynamic viscous incompressible flow of an electrically conducting Newtonian polymeric fluid from a moving permeable horizontal stretching sheet with variable magnetic field, momentum and thermal slip boundary conditions. The emerging nonlinear ordinary differential boundary value problem is solved numerically by the Runge-Kutta-Fehlberg fourth-fifth order numerical method in Maple symbolic software. The effects of the governing parameters on the dimensionless stream function, dimensionless flow velocity and the dimensionless temperature have been investigated, displayed graphically and discussed. It is found that greater momentum slip and magnetic field parameters reduce the dimensionless velocity. It is further observed that higher values of Prandtl number, thermal slip, and conductionradiation parameter (weaker radiation contribution) reduce the dimensionless temperature whilst stronger magnetic field increases the temperature due to the supplementary work expended in dragging the polymer against the action of the magnetic field which is dissipated as heat. Comparisons of numerical results with previous published results show an excellent agreement. The study finds applications in electro-conductive polymer (ECP) processing systems.

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.

Optimization of mass and heat flux of MHD viscous fluid flow with constant proportional Caputo derivative by using response surface methodology: Sensitivity analysis

The study of viscous dissipation in the context of unsteady incompressible magnetohydrodynamic viscous fluid flow over a moving plate is a complex and important topic in fluid dynamics and heat transfer. This scenario combines several physical phenomena and has practical applications in various engineering and scientific fields. The fractional mathematical model is proposed by considering the effect of viscous dissipation force of the flowing fluid. For this purpose, fluid is assumed to be lying over a vertical plate that is moving in its own plane. The governing equations are transformed into the dimensionless form and developed fractional model with a new operator Constant Proportional Caputo Derivative. We used the Laplace transform technique to find the solution of the dimensionless governing equation analytically. The transformed solutions for energy and momentum balances developed in terms of series. The validation of the present model comparison graphs is plotted for temperature. The sensitivity of different input parameters on output response are analyzed and displayed the sensitivity results in tabular and graphical form and found that the permeable parameter is most sensitive to skin friction coefficient, and the Eckert number is most sensitive parameter among others to Nusselt Number. The novelty of present work is to develop a correlation between input parameters and output responses by using Response Surface Methodology (RSM). As no such correlation has been developed for optimization of mass and heat flux of MHD viscous fluid flow with Constant Proportional Caputo derivative by using RSM. By using this correlation, we have performed sensitivity analysis for output responses.

A Hermite-type collocation mesh-free approach for simulating incompressible viscous fluid flows

In this work, a novel Hermite-type mesh-free model for incompressible viscous fluid flows is proposed, as a way, to overcome the numerical difficulties experienced by solving under weak or strong formulation the pure stream-function Navier–Stokes equation. In this model a dimensionless virtual domain is utilized, in order to make an accurate dimensionless shape-functions of the recently developed Hermite-type collocation Weighted Least Square approximation, by using dimensionless scale parameters. Then, a Jacobian transformation matrix is built to express the shape-functions spatial derivatives from the virtual to the considered domain. The resolution of the obtained nonlinear algebraic system is performed by the High Order Continuation Method. Numerical tests were investigated on incompressible viscous isothermal fluid flows in lid-driven cavity, backward-facing step, sudden expansions and around various obstacle shapes. They show the advantages of the proposed model compared to the reference Hermite-type collocation models used for pure stream-function equation and the weak Galerkin procedures as Finite Element Method and Element Free Galerkin method, in term of computation accuracy, number of degree of freedom, implementation simplicity and computation time. The numerical and experimental results of literature confirm the validity and capability of the proposed dimensionless model to simulate fluid flows in a expended-lengths inflow–outflow geometry and around obstacles of circular, inclined elliptical and Joukowski airfoil shapes.

A conservative sharp interface method for incompressible viscous two-phase flows with topology changes and large density ratio

Topology change of interfaces often leads to unresolved interface structures such as tiny droplets/bubbles, which requires the regularization of the order parameter and consequently causes artificial modification of volume fraction of the fluids. This could give rise to unphysical oscillation of pressure and cause the failure of computation, in particular for two-phase flows involving large density ratio. We develop a robust conservative sharp-interface method for incompressible viscous two-phase flows with topology changes and large density ratio. The method consists of a cut-cell meshing approach that dynamically generates unstructured meshes in the vicinity of the interface, a second-order finite volume scheme in the Arbitrary Lagrangian–Eulerian framework, and a projection method. The jump conditions at the interfaces are incorporated into the calculation of fluxes at the cell faces of the unstructured meshes that coincide with the reconstructed interfaces, to ensure that they are strictly satisfied at the interface. Unlike a pseudo-compressible formulation used in the previous study, the projection method prevents the oscillation of pressure in the presence of topology change. Special treatments are proposed to further improve the robustness of the method when dealing with unresolved interface structures, including removal of tiny droplets, adjustment of spatial discretization and restriction of the maximum curvature calculated. In such a way, two-phase flows involving topology change and large density ratio can be numerically resolved in a sharp-interface, efficient and robust manner. The performance of the proposed method is systematically examined by a series of numerical tests, including spurious currents, oscillation of a suspended droplet, droplet deformation in shear flows, breakup of a liquid thread, rising bubbles and partial coalescence of a droplet with a pool. The numerical results are compared against analytical solution, benchmark results or experimental data, and good agreement has been achieved.

Effect of the Non-Linear Radiative Unsteady Mixed Convective Flow over a Curved Stretching Surface with Soret and Dufour Effects: A Numerical Study

The subject of unsteady convective flow with non-linear thermal radiation has become an important issue of research, due to its implications in advanced energy conversion systems operating at high temperature, solar energy technology and chemical process at high operation temperature. Due to the importance of this issue, a time dependent incompressible viscous fluid flow, heat and mass transfer over a curved stretching surface has been numerically analysed by taking into account the heat flux due to concentration gradient and mass flux due to temperature gradient. Together with this the Rosseland approximation is being employed for the nonlinear thermal radiation impact in presence of thermal slip. With the aid of non-dimensional variables and the corresponding physical boundary conditions, the leading nonlinear momentum, energy, and species equations are converted into a set of coupled ordinary differential equations. These equations are then resolved using the MATLAB bvp4c solver. The stability of the numerical technique has been verified and compared with available literatures. The resultant parameters of engineering interest and the boundary layer flow field parameters and have been presented using tables and graphically plots. The study concludes that for lesser curvature parameter (0.5≤K≤0.7) the surface drag force, heat and mass transfer rates can improve by about 9.59%, 2.87% and 1.67% each respectively. The presence of the temperature ratio parameter and the non-linear thermal radiation are found to greatly influence the temperature profile and the heat transfer rate of the system. Results show that the heat transfer rate improves by about 24.39% and 16.66% for varying non-linear thermal radiation (1≤Rd≤1.5) and temperature ratio parameter (1.2≤θw≤1.4) respectively. Results obtained also show that improving the thermal slip parameter (0.4≤L≤0.6) can reduce heat transfer rate by about 13.62% and reduce the surface temperature profile.

Time-Dependent MHD Free Convective Heat Circulation of Hybrid Nano Liquid over a Vertical Porous Plate Due to Temperature Oscillation with Thermal Radiation and Viscous Dissipation

In the current numerical simulation, the thermal transfer of viscous incompressible time dependent MHD free convective flow of hybrid nanofluid (Cu-TiO2-H2O) over a vertical porous plate with viscous dissipation and thermal radiation is examined. The system of partial differential equations which controls the fluid flow are transmuted into dimensionless equations and are solved using numerical simulation namely Galerkin Finite Element Method. The momentum and thermal consequences, coefficient of heat transfer and skin friction with Gr, M, Ec, N, t, ωt, δ2, λ – parameters for both nanofluid (Cu-H2O) and hybrid nanofluid (Cu-TiO2-H2O) flows are exposed through graphs and tables. It is revealed that heat transfer coefficient of Cu-TiO2-H2O is more effective when compared with Cu-H2O flows varying with aforementioned parameters. The current numerical computation is in good agreement with the analytical solution of the problem. This study is used in several engineering fields such as electronic cooling, heat exchangers, nanomaterial processing, environmental engineering, chemical industry.

Asymptotic behavior of a viscous incompressible fluid flow in a fractal network of branching tubes

<p>We considered a viscous incompressible fluid flow in a varying bounded domain consisting of branching thin cylindrical tubes whose axes are line segments that form a network of pre-fractal curves constituting an approximation of the Sierpinski gasket. We supposed that the fluid flow is driven by volumic forces and governed by Stokes equations with boundary conditions for the velocity and the pressure on the wall of the tubes and inner continuity conditions for the normal velocity on the interfaces between the junction zones and the rest of the pipes. We constructed local perturbations, related to boundary layers in the junction zones, from solutions of Leray problems in semi-infinite cylinders representing the rescaled junctions. Using $ \Gamma $-convergence methods, we studied the asymptotic behavior of the fluid as the radius of the tubes tends to zero and the sequence of the pre-fractal curves converges in the Hausdorff metric to the Sierpinski gasket. Based on the constructed local perturbations, we derived, according to a critical parameter related to a typical Reynolds number of the flow in the junction zones, three effective flow models in the Sierpinski gasket, consisting of a singular Brinkman flow, a singular Darcy flow, and a flow with constant velocity.</p>

Dissipation in nonequilibrium thermodynamics and its connection to the Rayleighian functional

We examine quantitatively the role of dissipation in nonequilibrium thermodynamics and its connection to variational principles and the Rayleighian functional. The extremum of the Rayleighian is sometimes used to describe the inertialess (dissipation-dominated) dynamics of continuum systems, and it has been applied recently for the modeling of soft matter dynamics. We discuss how dissipation is considered within one of the modern complete descriptions of nonequilibrium thermodynamics, namely the single generator bracket formalism. Within this formalism, dissipation is introduced through the use of the dissipation bracket, describing irreversible dynamics, which is added to a Poisson bracket that describes the reversible dynamics of the system. A possible connection with the Rayleighian functional is then demonstrated that in all cases considered herein, the Rayleighian is equal to minus one half of the effective dissipation rate of the Lagrangian functional. The effective dissipation rate is obtained starting with an inertial (i.e., flux-based or velocity-based) system description, involving the Poisson bracket and the primitive part (i.e., without the entropy correction term) of the dissipative bracket. Several examples are discussed in detail, ranging from an algebraic model (damped oscillator) to continuum ones: modeling of fluid flow in porous particle media, viscous Newtonian compressible and incompressible fluid flows, and more interestingly, flow of a nematic liquid-crystalline material.

Numerical way out through finite volume method for Navier-Stokes type blood flow inside stenosed curved arteries

This article explores the intricate fluid dynamics within stenosed curved arteries, focusing on Newtonian or viscous fluids' incompressible, two-dimensional, and time-independent flow. The modeled Navier-Stokes equations in curvilinear coordinates are solved numerically through the finite volume method by using open foam, and exact solutions are also computed after using the assumptions of mild stenosis. The flow inside a stenosed curved artery having computational results through FVM is the main achievement of the present work. We have included 2D and 3D graphics depicting pressure gradient, velocity distribution, and shear stress for physical visualization. This helps provide a clear understanding of the physical circumstances exhibited in the analysis. This work contributes significantly to biomechanics by unraveling the intricacies of fluid flow in stenosed curved arteries. The combination of numerical simulations, exact solutions, and visual representations enhances our understanding of the underlying physical phenomena, paving the way for further advancements in cardiovascular research and clinical applications. These visual representations serve as crucial tools for physical visualization, enhancing the interpretability of the complex flow patterns observed in the analysis.

Decay properties of the Stokes semigroup for two-phase incompressible viscous flows

Decay properties of the Stokes semigroup for two-phase incompressible viscous flows

Analytical Approach to Nonlinear Oscillatory Flow Through a Semi-Infinite Vertical Permeable Wall in a Porous Medium with MHD Mixed Convection

The present work illustrates mixed MHD convection flow of an unstable two-dimensional viscous incompressible fluid flow in a porous material under the following conditions: semi-infinite vertical permeable wall support (i) There is a constant mean oscillation in the suction velocity normal to the wall throughout time. (ii) A constant mean velocity of the free stream; (iii) a constant wall temperature; and (iv) a somewhat high temperature differential between the wall and the free stream, which generates free convection currents. Conservation of mass, energy and momentum are used to obtain the governing equations. These equations are non-linear in nature and connected with one another. The nonlinear differential equations are non-dimensionalized employing non-dimensionalized parameters such as Prandtl number Pr, Grashof number Gr, Eckert number Ek, Hartmann number Mh, and Viscous ratio. An analytical method is used to solve approximate solutions for nonlinear PDEs utilizing the double regular perturbation technique. The numerical results for temperature, skin friction, heat flow, velocity, and skin friction are computed for various parameters and are demonstrated to be in good agreement with previous findings.

Interfacial vorticity dynamics for Navier–Stokes–Korteweg system: General theory and application to two-dimensional near-wall cavitation bubble

A theory of interfacial vorticity dynamics is developed for the single-component liquid–vapor flows described by the Navier–Stokes–Korteweg equations. The non-ideal equation of state and surface capillarity are collectively considered via the chemical potential gradient force. Explicit formulas of the interfacial enstrophy and chemical potential fluxes are derived to elucidate their generation mechanisms from the interface, which are expressed by using the fundamental surface physical quantities. Then, the transport equation of the Lamb dilatation (namely, the Lamb vector divergence) is rigorously derived, generalizing the previous results of the Lamb-vector dynamics for single-phase incompressible viscous flows. The derived results are evaluated in a near-wall cavitation bubble combined with the van der Waals equation of state. The roles of surface shear stress and vorticity, surface chemical potential gradient, surface acceleration, surface stretching-shrinking motion and dilatational waves are emphasized in generating the interfacial enstrophy and chemical potential fluxes, featured by the strong vorticity concentration, interface deformation and inward-propagating microjet due to the longitudinal pressure difference. These distinct dynamical features observed near the bubble interface are well captured by the spatial distribution of the Lamb dilatation. Analyzing the dynamics of the Lamb dilatation based on the transport equation demonstrates the significance of the high-curvature rotating surface region and its vicinity in view of their dominance to the unsteady diffusion effect of the Lamb dilatation. The present exposition could provide new physical insights into liquid–vapor flows from the perspective of interfacial vorticity dynamics.

Correlation between skin friction and enstrophy convection velocity in near-wall turbulence

The enstrophy convection velocity (denoted by uΩ) in the evolution equation of the boundary enstrophy is proportional to skin friction (denoted by τ) in an incompressible viscous flow, which can be determined globally as an optical flow problem from a time sequence of the boundary enstrophy fields. The correlation coefficient between |uΩ| and |τ| is evaluated in a turbulent channel flow at the friction Reynolds number Reτ=180, which is about 0.73 in the region of interest containing near-wall strong wall-normal velocity event associated with a sweep-ejection pair) and is approximately independent of the wall-normal coordinate in the viscous sublayer. This correlation coefficient is contributed mainly by strong near-wall coherent structures with high boundary enstrophy. The statistics of the difference between the normalized |uΩ| and |τ| are discussed. The statistical correlation between uΩ and τ elucidates the connection between near-wall flow structures and skin friction.

Numerical simulation for MHD flow of Powell Eyring nanofluid with heterogeneous–homogeneous reactions, Arrhenius energy over a variable thickness stretching surface

The paper deals with the viscous incompressible flow of Powell Eyring type nanofluid over a variable thicker stretching surface induced by heterogeneous-homogeneous reaction and Arrhenius activating energy in a porous medium. Brownian motion and thermophoresis effect also considered to define flow regime. Boundary layer approximations of the governed flow are described by the partial differential equations which are laidback to handle by reducing them into coupled nonlinear ordinary differential equations. A MATLAB package BVP 4c is used to simulate the equations very contentedly to describe the behavior of several parameters graphically. Impact of several governing parameters are discussed. Rationality of the resolution is scrutinized by the comparison with previous literature in Tables 1 and 2. Numerical values of the Nusselt number and Sherwood parameters are discussed in Table 3. velocity profile diminishes for magnetic parameter, variable thickness, first slip and second slip parameters. while uplifted for mixed convection parameter. Temperature profile tumbling for Prandtl number and uplifted for radiation parameter, Brownian motion, thermophoretic effects, Grashof number and Magnetic field effects. Concentration profile declines for Schmidt number, chemical species and homogeneous heterogenous parameters.

Analysis of incompressible viscous fluid flow in convergent and divergent channels with a hybrid meta-heuristic optimization techniques in ANN: An intelligent approach

Analysis of incompressible viscous fluid flow in convergent and divergent channels with a hybrid meta-heuristic optimization techniques in ANN: An intelligent approach

An efficient isogeometric/finite-difference immersed boundary method for the fluid–structure interactions of slender flexible structures

In this contribution, we present a robust and efficient computational framework capable of accurately capturing the dynamic motion and large deformation/deflection responses of highly-flexible rods interacting with an incompressible viscous flow. Within the partitioned approach, we adopt separate field solvers to compute the dynamics of the immersed structures and the evolution of the flow field over time, considering finite Reynolds numbers. We employ a geometrically exact, nonlinear Cosserat rod formulation in the context of the isogeometric analysis (IGA) technique to model the elastic responses of each rod in three dimensions (3D). The Navier–Stokes equations are resolved using a pressure projection method on a standard staggered Cartesian grid. The direct-forcing immersed boundary method is utilized for coupling the IGA-based structural solver with the finite-difference fluid solver. In order to fully exploit the accuracy of the IGA technique for FSI simulations, the proposed framework introduces a new procedure that decouples the resolution of the structural domain from the fluid grid. Uniformly distributed Lagrangian markers with density relative to the Eulerian grid are generated to communicate between Lagrangian and Eulerian grids consistently with IGA. We successfully validate the proposed computational framework against two- and three-dimensional FSI benchmarks involving flexible filaments undergoing large deflections/motions in an incompressible flow. We show that six times coarser structural mesh than the flow Eulerian grid delivers accurate results for classic benchmarks, leading to a major gain in computational efficiency. The simultaneous spatial and temporal convergence studies demonstrate the consistent performance of the proposed framework, showing that it conserves the order of the convergence, which is the same as that of the fluid solver.

Weakly viscous two-dimensional incompressible fluid flows using efficient isogeometric finite element method

This paper presents a straightforward and efficient numerical simulation method for solving the Navier–Stokes equations for weakly viscous incompressible fluids describing steady flow. Our approach utilizes isogeometric finite elements to handle higher-order partial differential operators associated with weakly viscous incompressible flow problems. Specifically, our numerical formulation employs a principle of virtual power (PVP)-based weak formulation that utilizes a stream-function field, which distinguishes it from the more commonly used bi-harmonic type formulations. The usage of a stream-function field ensures a pointwise divergence-free velocity condition, making the present method suitable for low to moderately high Reynolds number flow problems. In contrast to the bi-harmonic formulation, which is typically used for describing internal flow and requires special treatment of outflow boundary conditions, the PVP-based formulation is more general and does not require special treatment at the outflow boundary. It is also demonstrated that both bi-harmonic and PVP-based weak formulations yield identical results for internal flow problems. Our method employs non-uniform rational B-spline basis functions, and we present a simple stitching technique for imposing no-slip Dirichlet boundary conditions. Finally, we solve Poisson's equation to recover the pressure field. Furthermore, we use an appropriate Gaussian quadrature that is exact for splines to speed up the computation of various element matrices, especially for high polynomial degrees. The proposed formulation is evaluated by solving a set of numerical problems, including internal flow and channel flow problems.

A Gaussian–cubic backward substitution method for the four-order pure stream function formulation of two-dimensional incompressible viscous flows

A Gaussian–cubic backward substitution method for the four-order pure stream function formulation of two-dimensional incompressible viscous flows

Numerical investigation on self-propelled hydrodynamics of squid-like multiple tentacles with synergistic expansion

Cephalopods, such as squids, have versatile swimming mechanisms that allow them to adapt to complex underwater environments. Their primary means of propulsion are funnel jets, whereas coordinating soft wrists are often overlooked. The purpose of this study is to provide tentacles at the end of a squid-like robot with a circular symmetric expansion based on the traveling wave motion law and analyze the effects of the number, frequency and expansion amplitude of tentacles on its self-propelled performance. The geometry of the aquatic squid and flexible posterior segment including three joints are considered to be the key features. Overlapping grids of hole cutting technique are applied to manipulate virtual swimmers and simulate incompressible viscous flow. The results indicate that the three-tentacled squid has the best propulsion performance, and excessive tentacles cannot unilaterally enhance propulsion. The increase in frequency can be effectively mapped as an increase in the steady-state velocity coefficient and propulsion efficiency, whereas the maximum amplitude of the tentacle bending could only be raised within a certain range, and excessive bending may be counterproductive. The corresponding flow structure can indirectly reveal the evolution process of the multi-tentacled expansion performance.