Two-dimensional Fluid Flow Problems Research Articles

Applications of differential subordination and superordination theorems to fluid mechanics involving a fractional higher-order integral operator

The paper aims to study differential subordination and superordination preserving properties for certain analytic multivalent functions within the open unit disk related to a novel generalized fractional derivative operator for higher-order derivatives. As an application, we provide an explicit construction for the complex potential (the complex velocity) and the stream function of two-dimensional fluid flow problems over a circular cylinder using both vortex and source/sink. We further determine the fluid flow produced by a single source and construct a univalent function so that the image of a source is also a source for a given complex potential. Finally, we present some plot simulations that illustrate the results of this work.

Flow characteristics and flow-induced forces of a stationary and rotating triangular cylinder with different incidence angles at low Reynolds numbers

In this paper, the problem of two-dimensional fluid flow past a stationary and rotationally oscillating equilateral triangular cylinder with a variable incident angle, Reynolds number, oscillating amplitude, and oscillating frequency is numerically investigated. The computations are carried out by using a two-step Taylor-characteristic-based Galerkin (TCBG) algorithm. For the stationary cases, simulations are conducted at various incident angles of α=0.0–60.0° and Reynolds numbers of Re=50–160. For the oscillation cases, the investigations are done at various oscillating amplitudes of θmax=7.5–30.0° and oscillating frequencies of Fs/Fo=0.5–3.0 considering two different incidence angles (α=0.0°, 60.0°) and three different Reynolds numbers (Re=50, 100, 150). The results show that the influences of key parameters (incidence angle, Reynolds number, oscillating amplitude, and oscillating frequency) are significant on the flow pattern and hydrodynamic forces. For the stationary cases, at smaller angle of incidence (α≤30.0°), Reynolds number has a large impact on the position of the separation points. When α is between 30.0° and 60.0°, it was found that the separation points are located at the rear corners. From a topological point of view, the diagram of flow pattern is summarized, including two distinct patterns, namely, main separation and vortex merging. A deep analysis of the influence of Reynolds number and incidence angles on the mean pressure coefficient along the triangular cylinder surface is presented. Additionally, for the oscillating cases, the lock-on phenomenon is captured. The dominant flow patterns are 2S mode and P+S mode in lock-on region at α=0.0°. It is found at α=60.0°, however, that the flow pattern is predominantly 2S mode. Furthermore, except for the case of Fs/Fo=2.0, the mean drag decreases as the oscillating amplitude increases for each Reynolds number at α=0.0°. At α=60.0°, the minimum mean drag for Fs/Fo=1.5 is lower than that for stationary case, and occurs at θmax=15.0° (Re=100) and θmax=22.5° (Re=150), respectively. Finally, the effect of Reynolds number on a rotational oscillation cylinder is elucidated.

Integrated radial-basis-function networks for computing Newtonian and non-Newtonian fluid flows

This paper presents a radial-basis-function (RBF) collocation method for the simulation of two-dimensional fluid-flow problems. To improve the stability of a discrete solution and the quality of derivative approximations, the present RBF networks (RBFNs) are constructed through integration instead of conventional differentiation. Special attention is given to the following two topics: (i) the effective use of integration constants in the solution of the Navier–Stokes equations and (ii) the employment of “local” integrated RBFNs to handle flows with fine structures. Different types of geometries and fluids are considered. The accuracy of the present technique is demonstrated through the solution of several benchmark test problems.

Application of meshless EFG method in fluid flow problems

This paper deals with the solution of two-dimensional fluid flow problems using the meshless element-free Galerkin method. The unknown function of velocity u(x) is approximated by moving least square approximants uh(x). These approximants are constructed by using a weight function, a monomial basis function and a set of non-constant coefficients. The variational method is used for the development of discrete equations. The Lagrange multiplier technique has been used to enforce the essential boundary conditions. A new exponential weight function has been proposed. The results are obtained for a two-dimensional model problem using different EFG weight functions and compared with the results of finite element and exact methods. The results obtained using proposed weight functions (exponential) are more promising as compared to those obtained using existing weight functions (quartic spline and Gaussian)

MODIFIED SIMPLE FORMULATION ON A COLLOCATED GRID WITH AN ASSESSMENT OF THE SIMPLIFIED QUICK SCHEME

The simplified QUICK scheme (transverse curvature terms are neglected) is extended to a nonuniform, rectangular, collocated grid system for the solution of two-dimensional fluid flow problems using a vertex-based finite-volume approximation. The influence of the non-pressure gradient source term is added to the Rhie-Chow interpolation method [5], and a local-mode Fourier analysis of the modified scheme demonstrates that characteristically, it is strongly elliptic and has high-frequency damping capability, which effectively eliminates the grid-scale pressure oscillations. Within this framework, the SIMPLE iteration procedure is constructed. A comparison between the present method and the control-volume-based finite-element method (CVFEM) with vorticity-stream function formulation for free convection in a cavity indicates that the proposed scheme can be applied successfully to fluid flow and heat transfer problems.

The problem of a gas bubble in plane ideal fluid flow

We study the problem of two-dimensional fluid flow past a gas bubble adjacent to an infinite rectilinear solid wall. Two-dimensional ideal fluid flow past a gas bubble on whose boundary surface-tension forces act (or a gas bubble bounded by an elastic film) has been studied by several authors. Zhukovskii, who first studied jet flows with consideration of the capillary forces, constructed an exact solution of the problem of symmetric flow past a gas bubble in a rectilinear channel [1]. However, Zhukovskii's solution is not the general solution of the problem; in particular, we cannot obtain the flow past an isolated bubble from his solution. Slezkin [2] reduced the problem of symmetric flow of an infinite fluid stream past a bubble to the study of a nonlinear integral equation. The numerical solution of this problem has recently been found by Petrova [3]. McLeod [4] obtained an exact solution under the assumption that the gas pressure p1 in the bubble equals the flow stagnation pressure p0. Beyer [5] proved the existence of a solution to the problem of flow of a stream having a given velocity circulation provided p1≥p0. We examine the problem of two-dimensional ideal fluid flow past a gas bubble adjacent to an infinite rectilinear solid wall. The solution depends on the value of the contact angle βπ. The existence of a solution is proved in some range of variation of the parameters, and a technique for finding this solution is given. The situation in which β=1/2 is studied in detail.