Boundary-layer flow of the power-law fluid over a moving wedge: a linear stability analysis

We study the stability of the two-dimensional boundary-layer flow of a power-law (Ostwald de Waele) non-Newtonian fluid over a moving wedge. The mainstream velocity is assumed to have a power of distance from the leading boundary layer, such that the system admits to the self-similar solutions. We discuss the problem in question for both shear-thickening and shear-thinning fluids which lead to a non-uniqueness (double solutions) in the base flow solutions. We then address an issue of the stability of the non-unique solutions. A linear eigenvalue analysis of the double solution reveals that the basic flow represented by the first solution is always stable, and this flow is practically encountered. The system becomes unstable to the second solutions which have the mode-two perturbations with larger boundary-layer thickness. The first and second solutions form a tongue-like structure in the solution space. Furthermore, the modification of the viscosity for the power-law fluids reveals that the system predicts an infinite viscosity in the confinement of the boundary-layer region. Extensive comparisons of the solutions with the existing models with Newtonian fluid are made, and a physical explanation behind these solutions is proposed.

     

Numerical simulation of separating boundary-layer flow

A two-dimensional boundary-layer flow over a bump has been studied computationally by solving the incompressible Navier–Stokes equations. The numerical solution procedure uses a mapping transforming the physical coordinate system into a Cartesian one. The resulting system is solved using a mixed finite differences––Chebyshev collocation discretization. We compare the influence matrix technique with a fractional time-step procedure used to enforce the divergence-free condition. Numerical experiments are performed for bumps with different aspect ratios. The separation structure is investigated for increasing Reynolds number and self-induced vortex shedding is reproduced numerically.     

Numerical simulation for MHD flow of Sisko nanofluid over a moving curved surface: A revised model

Microsystem Technologies - An analysis regarding diverse features of Sisko fluid flow over a curved stretching surface in the presence of magneto-nanoparticles is presented. For larger value of the...     

Analysis of non-linear radiative stagnation point flow of Carreau fluid with homogeneous-heterogeneous reactions

Microsystem Technologies - Current work focuses on stagnation point flow of MHD Carreau fluid with heterogeneous–homogeneous reactions. Non-linear stretched sheet of variable thickness is the...     

Modeling of fluid flow in a tube with a moving indentation

The time-dependent flow in a tube with a moving indentation is numerically simulated using a dynamic mesh model. The model was used to simulate the flow in a tube with an indentation moving at different frequencies. The model was validated for a two-dimensional channel with a moving indentation. The results exhibited good agreement with the available experimental results. The results show that a single vortex was formed at a wall frequency of 0.1 Hz and was swept out of the tube at the end of the period. At a higher frequency of 1 Hz, vortex doubling occurred with reverse flow dominating downstream of the indentation. The results also show that the wall shear stress was larger for the higher frequency case of the moving indentation.     

Numerical method and results for inviscid supersonic flow over a compressive ramp

An algorithm is presented for the steady, two-dimensional, inviscid, supersonic flow near a wall with a compressive turn. The wall is contoured to provide a centered, Prandtl-Meyer compression. The focal point of the compression is the origin of an oblique shock wave, a slipstream and a secondary disturbance. This disturbance is an expansion, a weak solution oblique shock, or a strong solution oblique shock. Although algebraic equations govern the flow in the vicinity of the focal point, a sophisticated algorithm is required for the solution, which does not always exist and is not always unique. For a range of incident Mach numbers ranging from 1.2 to 16, the near-field solution is compared with its well-known asymptotic far-field counterpart.     

Falkner–Skan wedge flow of a power-law fluid with mixed convection and porous medium

This article describes the mixed convection flow of a non-Newtonian fluid past a wedge. An incompressible power-law fluid occupies the porous space. The arising mathematical problem has been solved by homotopy analysis method (HAM). Convergence of the derived solution is checked. The local skin friction coefficient and Nusselt number are also discussed.     

Incompressible flow computations over moving boundary using a novel upwind method

In this paper a novel method for simulating unsteady incompressible viscous flow over a moving boundary is described. The numerical model is based on a 2D Navier–Stokes incompressible flow in artificial compressibility formulation with Arbitrary Lagrangian Eulerian approach for moving grid and dual time stepping approach for time accurate discretization. A higher order unstructured finite volume scheme, based on a Harten Lax and van Leer with Contact (HLLC) type Riemann solver for convective fluxes, developed for steady incompressible flow in artificial compressibility formulation by Mandal and Iyer (AIAA paper 2009-3541), is extended to solve unsteady flows over moving boundary. Viscous fluxes are discretized in a central differencing manner based on Coirier’s diamond path. An algorithm based on interpolation with radial basis functions is used for grid movements. The present numerical scheme is validated for an unsteady channel flow with a moving indentation. The present numerical results are found to agree well with experimental results reported in literature.     

Numerical modelling of wind flow over a complex topography

Numerical modelling of wind flow over complex dune topography is an ambitious prospect. There is an increasing need to understand wind flow over complex topography for land planning purposes to enable prediction of sediment transport at a particular site. New surveying techniques permit the rapid development of digital terrain models, however a stumbling block is the ability of Computational Fluid Dynamics (CFD) to emulate the wind flow over such a landscape. To overcome these difficulties, it is important to establish the parameters within which such simulations can operate. This paper details an initial two-dimensional numerical model developed in order to test various modelling assumptions against experimental field wind data. Mason Bay, Stewart Island, New Zealand was chosen as an undisturbed but accessible experimental site with a prevalent on-shore wind perpendicular to a simple foredune and a complex down-wind parabolic dune system. A complex topographical two-dimensional model with vegetation represented as a roughness was compared against field data along a transect dissecting a dune system.This paper establishes that:

* Replicating the roughness patterns at the surface is important

* The inlet profile should be duplicated with care

* Modelling only a portion of the domain can have an effect on the flow patterns due to outflow effects

* There is a modelling decision to be made between the complexity of the topography and the sophistication of the turbulence model and degree to which vegetation and sand transportation are modelled.

The long-term aim is to instil confidence in numerical techniques so that such technology can be used for predictive purposes.     

Lie-group similarity solution and analysis for fractional viscoelastic MHD fluid over a stretching sheet

Lie-group is introduced for studying boundary layer flow and heat transfer of fractional viscoelastic MHD fluid over a stretching sheet. Fractional boundary layer equations, based on Riemann–Liouville operators, are reduced and solved numerically by Grünwald scheme approximation. Results show that the skin friction and thermal conductivity are strongly affected by magnetic field parameter, fractional derivative and wall stretching exponent. The bigger of the fractional order derivative leads to the faster velocity of viscoelastic fluids near the plate but not to hold near the outer flow. Skin friction increases with increase of magnetic field parameter $M$, while the heat transfer decreases. For wall stretching exponent parameter $\beta =1.0$, the velocity profile decreases with the increase of similarity variable $\eta$. However, for $\beta =?1.5$, the velocity profile increases initially and then decreases afterwards with the biggest velocity at the interior of boundary layer.     

The optimal solution for the flow of a fourth-grade fluid with partial slip

The steady flow of a non-Newtonian fluid when slippage between the plate and the fluid occurs is considered. The constitutive equations of the fluid are modeled for a fourth-grade non-Newtonian fluid with partial slip; they give rise to nonlinear boundary value problems. Analytical solutions are obtained using powerful analytic techniques for solving nonlinear problems, homotopy perturbation and optimal homotopy asymptotic methods. The results obtained are compared with the numerical results and it is shown that solutions exist for all values of the non-Newtonian parameters. The solutions valid for the no-slip condition for all values of the non-Newtonian parameters can be derived as special cases of the present analysis. Finally the solutions are discussed using a graphical approach.     

Numerical solution for two-dimensional flow in a branching channel using boundary-fitted coordinates

A numerical method is presented for the 2-D flow of a viscous, incompressible fluid in a branching channel. The problem has previously been solved by Bramley and Dennis [1] for restricted values of the branching angle and relative channel widths. Here a curvilinear coordinate generation algorithm is used to map the solution region onto a rectangle and this permits a solution over unrestricted ranges of branching angle and channel widths. The Navier-Stokes equations are solved in terms of stream function and vorticity using a difference scheme proposed by Dennis and Hudson [2]. Results are presented showing the effects on fluid separation of variations in Reynolds number, branching angle and relative channel widths upstream and downstream. Comparison is made with the earlier work by Bramley and Dennis [1].     

A finite element immersed boundary method for fluid flow around moving objects

This paper presents the extension of a recently proposed immersed boundary method to the solution of the flow around moving objects. Solving the flow around objects with complex shapes may involve extensive meshing work that has to be repeated each time a change in the geometry is needed. Mesh generation and solution interpolation between successive grids may be costly and introduce errors if the geometry changes significantly during the course of the computation. These drawbacks are avoided when the solution algorithm can tackle grids that do not fit the shape of immersed objects. This work presents an extension of our recently developed finite element Immersed Boundary (IB) method to transient applications involving the movement of immersed fluid/solid interfaces. As for the fixed solid boundary case, the method produces solutions of the flow satisfying accurately boundary conditions imposed on the surface of immersed bodies. The proposed algorithm enriches the finite element discretization of interface elements with additional degrees of freedom, the latter being eliminated at element level. The boundary of immersed objects is defined using a time dependent level-set function. Solutions are shown for various flow problems and the accuracy of the present approach is measured with respect to solutions on body-conforming meshes.     

A numerical investigation of fluid flow over a rotating cylinder with cross flow oscillation

This paper studies a two-dimensional incompressible viscous flow past a rotating cylinder with cross flow oscillation using a finite element method based on the characteristic based split (CBS) algorithm to solve governing equations including full Navier–Stokes and continuity equations. Dynamic unstructured triangular grid is used employing lineal and torsional spring analogy which is coupled with the solver by an Arbitrary Lagrangian–Eulerian (ALE) formulation. After verifying the accuracy of the numerical code, simulations are conducted for the flow past a rotating cylinder with cross flow oscillation at moderate Reynolds numbers of 50, 100, and 200 considering different non-dimensional rotational speeds based on the free-stream velocity in the range 0–2.5, and various oscillating amplitudes and frequencies. Effects of the oscillation and rotation of the cylinder on the vortex shedding both in lock-on and non-lock-on regions, the mean drag and lift coefficients, and the Strouhal number are investigated in detail. It is found that similar to the fixed cylinder beyond a critical non-dimensional rotational speed the vortex shedding is highly suppressed. In addition, by increasing the rotational speed of the cylinder, the lift coefficient increases while decreasing the drag coefficient. However, in the vortex lock-on region both the lift and the drag coefficients increase significantly.     

Numerical analysis and computations of a high accuracy time relaxation fluid flow model

We present a numerical study based on continuous finite element analysis for a time relaxation regularization of Navier–Stokes equations. This regularization is based on filtering and deconvolution. We study the convergence of the regularized equations using a fully discretized filter and deconvolution algorithm. Velocity and pressure error estimates and the L ₂ Aubin–Nitsche lift technique are proved for the equilibrium problem, and this analysis is accompanied by the velocity error estimate for the time-dependent problem, too. Thus, optimal error estimates in L ₂ and H ¹ norms are derived and followed by their computational verification. Also, computational results of the vortex street are presented for the two-dimensional cylinder benchmark flow problem. Maximum drag and lift coefficients and difference in pressure between the front and back of the cylinder at the final time were investigated as well, showing that the time relaxation regularization can attain the benchmark values.     

Numerical solution of incompressible flow through branched channels

The work deals with numerical solution of 3D turbulent flow in straight channel and branched channels with two outlets. The mathematical model of the flow is based on Reynolds-averaged Navier–Stokes equations for incompressible flow in 3D with explicit algebraic Reynolds stress turbulence model (EARSM). The mathematical model is solved by artificial compressibility method with implicit finite volume discretization. The channels have constant square or circular cross-section, where the hydraulic diameter is same in order to enable comparison between these numerical simulations. First, developed flow in a straight channel of square cross-section is presented in order to show the ability of the used EARSM turbulence model to capture secondary corner vortices, which are not predicted by eddy viscosity models. Next the flow through channels with perpendicular branch is simulated. Methods of setting the flow rate are discussed. The numerical results are presented for two flow rates in the branch.     

广义Maxwell流体分数阶微分方程的数值解法

针对广义Maxwell粘弹性流体分数阶微分方程,建立了一种隐式差分格式,给出了数值解的求解公式,证明了隐式差分格式稳定性与收敛性。     

Numerical solution of an electrically conducting viscous incompressible fluid

This paper investigates the flow pattern of an axisymmetric, electrically conducting viscous and incompressible fluid in a pipe, having a throat at its centre. An iterative finite difference method, based on Picards approximations for the spatial derivatives of the governing equations, is used to obtain the streamline patterns of the fluid flow field in presence of a magnetic field. An initial parabolic velocity profile is assumed at the entrance of the pipe. Numerical solutions which are computed for the values of Reynolds number lying between 50 and 2000 and the magnetic pressure number varying from 0 to 80 show the occurrence of a secondary flow in the downstream region and a recirculating flow in the upstream region of the pipe.     

Numerical study of the flow over shallow cavities

This paper reports on a series of numerical simulations of both laminar and turbulent flows over shallow cavities. For the turbulent case the influences of the following parameters were considered: (i) cavity aspect ratios, (ii) turbulence level of the oncoming flow, and (iii) Reynolds number. Several important results and conclusions are reported. We have found that for the turbulent case the external flow touches the floor of the cavity, and this depends on a specific value of each of these parameters. This condition has an important impact upon convective effects inside the cavity. The mathematical model corresponds to the incompressible, Reynolds-averaged, Navier-Stokes equations plus a high-Reynolds κ-ε model of turbulence, and the numerical computation is performed using the SIMPLER algorithm.