Transition to chaos in lid-driven square cavity flow

To date, there are very few studies on the transition beyond second Hopf bifurcation in a lid-driven square cavity, due to the difficulties in theoretical analysis and numerical simulations. In this paper, we study the characteristics of the third Hopf bifurcation in a driven square cavity by applying a consistent fourth-order compact finite difference scheme rectently developed by us. We numerically identify the critical Reynolds number of the third Hopf bifurcation located in the interval of (13944.7021,13946.5333) by the method of bisection. Through Fourier analysis, it is discovered that the flow becomes chaotic with a characteristic of period-doubling bifurcation when the Reynolds number is beyond the third bifurcation critical interval. Nonlinear time series analysis further ascertains the flow chaotic behaviors via the phase diagram, Kolmogorov entropy and maximal Lyapunov exponent. The phase diagram changes interestingly from a closed curve with self-intersection to an unclosed curve and the attractor eventually becomes strange when the flow becomes chaotic.     

Unsteady MHD free convective heat and mass transfer from a vertical porous plate with Hall current,thermal radiation and chemical reaction effects

An analysis is presented to investigate the effects of chemical reaction, thermal radiation and heat generation or absorption on unsteady free convective heat and mass transfer along an infinite vertical porous plate in the presence of a transverse magnetic field and Hall current. The governing partial differential equations are formulated and transformed by using a similarity transformation into a system of ordinary differential equations. The resulting equations are solved numerically using a fourth‐order Runge–Kutta scheme along with the shooting method. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. Numerical results for the velocity, temperature and concentration distributions are shown graphically for different parametric values. The effects of parameters on the local friction coefficients, the Nusselt number and Sherwood numbers are depicted in tabulated form. Copyright © 2009 John Wiley & Sons, Ltd.     

Unsteady CFD computations using vertex‐centered finite volumes for unstructured grids on Graphics Processing Units

This paper presents a Navier–Stokes solver for steady and unsteady turbulent flows on unstructured/hybrid grids, with triangular and quadrilateral elements, which was implemented to run on Graphics Processing Units (GPUs). The paper focuses on programming issues for efficiently porting the CPU code to the GPU, using the CUDA language. Compared with cell‐centered schemes, the use of a vertex‐centered finite volume scheme on unstructured grids increases the programming complexity since the number of nodes connected by edge to any other node might vary a lot. Thus, delicate GPU memory handling is absolutely necessary in order to maximize the speed‐up of the GPU implementation with respect to the Fortran code running on a single CPU core. The developed GPU‐enabled code is used to numerically study steady and unsteady flows around the supercritical airfoil OAT15A, by laying emphasis on the transonic buffet phenomenon. The computations were carried out on NVIDIA's Ge‐Force GTX 285 graphics cards and speed‐ups up to ～46 × (on a single GPU, with double precision arithmetic) are reported. Copyright © 2010 John Wiley & Sons, Ltd.     

Unsteady shrinking sheet with mass transfer in a rotating fluid

In this paper, the problem of unsteady flow induced by a shrinking sheet with mass transfer in a rotating fluid is studied. The transformed boundary layer equations are solved numerically by an implicit finite‐difference scheme known as the Keller‐box method. The influence of rotation, unsteadiness and mass suction parameters on the reduced skin friction coefficients f″(0) and g′(0), as well as the lateral velocity and velocity profiles are presented and discussed in detail. Copyright © 2010 John Wiley & Sons, Ltd.     

Cell face velocity alternatives in a structured colocated grid for the unsteady Navier–Stokes equations

The use of a colocated variable arrangement for the numerical solution of fluid flow is becoming more and more popular due to its coding simplicity. The inherent decoupling of the pressure and velocity fields in this arrangement can be handled via a special interpolation procedure for the calculation of the cell face velocity named pressure‐weighted interpolation method (PWIM) (AIAA J. 1983; 21 (11):1525–1532). In this paper a discussion on the alternatives to extend PWIM to unsteady flows is presented along with a very simple criterion to ascertain if a given interpolation practice will produce steady results that are relaxation dependent or time step dependent. Following this criterion it will be shown that some prior schemes presented as time step independent are actually not, although by using special interpolations can be readily adapted to be. A systematic way of deriving different cell face velocity expressions will be presented and new formulae free of Δt dependence will be derived. Several computational exercises will accompany the theoretical discussion to support our claims. Copyright © 2009 John Wiley & Sons, Ltd.     

MHD flow and heat transfer over permeable stretching sheet with slip conditions

The magnetohydrodynamic (MHD) flow and heat transfer characteristics for the boundary layer flow over a permeable stretching sheet are considered. Velocity and thermal slip conditions are taken into account. Problem formulation is developed in the presence of thermal radiation. Governing non‐linear problem is solved by a homotopy analysis method. Convergence of the derived solutions is studied. Numerical values of skin‐friction coefficient and local Nusselt number are tabulated. Effects of pertinent parameters on the velocity and temperature profiles are discussed. Comparison between the present and previous limiting results is shown. Copyright © 2010 John Wiley & Sons, Ltd.     

Unsteady hydromagnetic flow of a reactive variable viscosity third‐grade fluid in a channel with convective cooling

This paper examines the combined effects of a transverse magnetic field and variable viscosity on unsteady flow of a reactive third‐grade electrically conducting fluid and heat transfer in a channel with convective cooling at the surface. It is assumed that the fluid has small electrical conductivity and the electromagnetic force produced is very small. The coupled nonlinear partial differential equations governing the problem are derived and solved numerically using a semi‐implicit finite‐difference scheme. Both numerical and graphical results are presented and physical aspects of the problem are discussed with respect to various parameters embedded in the system. It is in general noted that those parameters that increase/decrase one flow quantity (velocity or temperature) also lead to the increase/decrease respectively of the other quantity. Copyright © 2011 John Wiley & Sons, Ltd.     

Three‐dimensional vortex simulation of unsteady flow in hydraulic turbines

On the basis of the Helmholtz decomposition, a grid‐free numerical scheme is provided for the solution of unsteady flow in hydraulic turbines. The Lagrangian vortex method is utilized to evaluate the convection and stretch of the vorticity, and the BEM is used to solve the Neumann problem to define the potential flow. The no‐slip boundary condition is satisfied by generating vortex sticks at the solid surface. A semi‐analytical regularization technique is applied to evaluate the singular boundary surface integrals of the potential velocity and its gradients accurately. The fast multipole method was extended to evaluate the velocity and velocity gradients induced by the discretized vortex blobs in the Lagrangian vortex method. The successful simulation for the unsteady flow through a hydraulic turbine's runner has manifested the effectiveness of the proposed method. Copyright © 2011 John Wiley & Sons, Ltd.     

A study of gridless method with dynamic clouds of points for solving unsteady CFD problems in aerodynamics

When solving unsteady computational fluid dynamics problems in aerodynamics with a gridless method, a cloud of points is usually required to be regenerated due to its accommodation to moving boundaries. In order to handle this problem conveniently, a fast dynamic cloud method based on Delaunay graph mapping strategy is proposed in this paper. A dynamic cloud method makes use of algebraic mapping principles and therefore points can be accurately redistributed in the flow field without any iteration. In this way, the structure of the gridless clouds is not necessarily changed so that the clouds regeneration can be avoided successfully. The spatial derivatives of the mathematical modeling of the flow are directly determined by using weighted least‐squares method in each cloud of points, and then numerical fluxes can be obtained. A dual time‐stepping method is further implemented to advance the two‐dimensional Euler equations in arbitrary Lagarangian–Eulerian formulation in time. Finally, unsteady transonic flows over two different oscillating airfoils are simulated with the above method and results obtained are in good agreement with the experimental data. Copyright © 2009 John Wiley & Sons, Ltd.     

棱柱绕流流动的数值模拟

利用数值方法对长宽比为1／3, 1和3的棱柱绕流在雷诺数为100的非稳态流动特性进行了分析和研究。采用有限体积法对棱柱绕流的二维流动N-S方程进行离散求解,分析和研究了非稳态的棱柱绕流流场,升力系数,阻力系数和涡动特性,数值模拟的结果与相关文献的数据比较吻合。通过上述研究能够为了解棱柱绕流的非稳态流动特性提供有力的帮助。而对棱柱三维流动的模拟分析和对雷诺数的变化对棱柱流动特性的影响进行研究,将为掌握棱柱绕流的工程特性打下基础。