Simulation of Separating Flows over a Backward-Facing Step

Simulation results are reported for plane two-dimensional viscous incompressible flow in a channel with an abrupt expansion. The mathematical model is provided by the quasi-hydrodynamic equations in the incompressible fluid approximation. The computations are carried out in a range of Reynolds numbers including both laminar and turbulent flow. As the Reynolds number increases, the solution bifurcates and the steady laminar flow changes to time-dependent flow. The computation results are consistent with known experimental data. Turbulence models were not used for large Reynolds number computations.     

Laminar flow separation in an axi-symmetric sudden smooth expanded circular tube

This paper concerns with the investigation of laminar flow separation and its consequences in a tube over a smooth expansion under the axi-symmetric approximations. A co-ordinate stretching has been made to map the expanded tube into a straight tube. The two-dimensional unsteady Navier-Stokes equations are solved approximately by using primitive variables in staggered grid. A thorough quantitative analysis is performed through numerical simulations of the desired quantities such as wall shear stress, axial velocity, pressure distribution etc. These quantities are presented graphically and their consequences in the flow field are analysed in details. The dependence of the flow field on the physical parameter like expansion height d and on the Reynolds number has been investigated in details. It is interesting to note that the peak value of wall shear stress decreases with increasing height of expansion and also with the increasing Reynolds number.     

On critical reynolds numbers in plane channels with a sudden expansion at the entry

A method for the numerical solution of fluid dynamics equations is proposed. The evolution of the structure of the laminar flow with increasing Reynolds number and its behavior at the critical Reynolds number Re_cris analyzed. Various flow modes at Re = Re_cr are discussed.     

Numerical Solution of Several Models of Internal Transonic Flow

The paper deals with numerical solution of internal flow problems. It mentions a long tradition of mathematical modeling of internal flow, especially transonic flow at our department. Several models of flow based on potential equation, Euler equations, Navier-Stokes and Reynolds averaged Navier-Stokes equations with proper closure are considered. Some mathematical and numerical properties of the model are mentioned and numerical results achieved by in-house developed methods are presented.     

Multi-Fracture Reservoir Simulations for Long Time Physical Processes

Reservoirs with multi-fracture techniques are developed and frequently used for oil and gas industry. Recently, they are also used for deep geothermal reservoirs especially for Hot Dry Rock (HDR). The analysis of the reservoir is generally interested in long time physical properties (10–100 years), e.g. fluid flow, heat transport etc. Typical CFD simulations are limited in this context. Here we developed a fluid flow and heat transport modeling in a multi-fracture reservoir based on the so-called Mixed Dimensional Model (MDM), which describes the different characteristic flows and the heat transport in different dimensions. In the mathematical point of view, these models are discretized based on the Cellular Automaton (CA) method combined with other necessary numerical techniques. The different cases of fluid flow and heat transport in multi-fracture reservoirs have been simulated and shown physical results very reasonably with less computational time. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical simulation and visualization of vortical structure transformation in the flow past a sphere at an increasing degree of stratification

Based on numerical simulation and visualization, the vortex structure of the flow past a sphere moving uniformly and horizontally in a linearly (density) stratified viscous fluid with an increasing degree of stratification (with the internal Froude number Fr decreasing from infinity to 0.005) at Re = 100 is analyzed in detail for the first time. The classification of the flow regimes is refined. The direct numerical simulation is based on the method of splitting with respect to physical factors (MERANZH) with an explicit hybrid finite-difference scheme, which is second-order accurate in space, monotone, and has a minimal numerical viscosity and dispersion.     

On the non-orthogonal Stagnation flow of the Oldroyd-B fluid

This paper is concerned with a non-orthogonal stagnation flow of an Oldroyd-B fluid between two parallel plates. We reduce the problem to a set of ordinary differential equations (ODE's), which is then solved with finite differences using a parameter continuation method. Perturbation analyses are also carried out for small Reynolds numbers and small Weissenberg numbers respectively. The solution of the set of ODE's is discussed. It is known that for a Newtonian fluid, the stagnation point shifts from the potential flow case in the opposite direction of the tangential velocity. The effect of the fluid elasticity is to reduce this shift. It is also shown that the Oldroyd-B model has a limiting Weissenbeg number, depending on the angle of the injected flow.     

Parametric study of liquid droplets impinging on porous surfaces

This work presents a numerical simulation of the fluid dynamics of a liquid droplet during impact/absorption onto a porous medium. The main focus of this paper is on a parametric study of the influence of the governing parameters upon the fluid flow characteristics. The problem is described in a non-dimensional form, and the influence of the main governing parameters is investigated, including their variation along the range of physical configurations of interest. This procedure revealed 7 main governing parameters: Reynolds number (Re), Darcy number (Da), porosity (ε), Froude number (Fr), Weber number (We), contact angle (θ) and the ratio between pore and particle diameter size in the porous substrate (α). The results indicate that the values of Da and Re are more related to the amount of momentum dissipation due to the drag of the solid matrix of the substrate, while the values of We, α and θ can be mainly related to capillary pressure.     

Non-local first-order modelling of crowd dynamics: A multidimensional framework with applications

In this work a physical modelling framework is presented, describing the intelligent, non-local, and anisotropic behaviour of pedestrians. Its phenomenological basics and constitutive elements are detailed, and a qualitative analysis is provided. Within this common framework, two first-order mathematical models, along with related numerical solution techniques, are derived. The models are oriented to specific real world applications: a one-dimensional model of crowd–structure interaction in footbridges and a two-dimensional model of pedestrian flow in an underground station with several obstacles and exits. The noticeable heterogeneity of the applications demonstrates the significance of the physical framework and its versatility in addressing different engineering problems. The results of the simulations point out the key role played by the physiological and psychological features of human perception on the overall crowd dynamics.     

Numerical investigation of vortical evolution in a backward-facing step expansion flow

A numerical investigation of laminar flow over a backward-facing step is presented for the Reynolds number in the range of 50Re2500. The objective of this numerical investigation is to add to the existing knowledge of the backward-facing step flow to deepen our understanding of the expansion flow structure. We proceed with the analysis by verifying the computer code through the Pearson vortex problem. We then perform a parametric study by varying the Reynolds number, with the aim of determining whether or not there exists a critical Reynolds number, above which reattachment length on the channel floor decreases. We also concentrate on subjects that have been little explored in the flow, examples of which are the onset of a single vortex in the primary eddy and how the recirculating bubble containing flow reversals is torn into smaller eddies. Eddy distortion, leading to mobile saddle points, and the merging of eddies are also discussed in this study.     

Numerical study on the fluid-structure interaction in a model aquatic canopy flow

This work presents numerical simulations and selected results of the flow over aquatic canopies, consisting of artificial flexible rectangular blades, arranged in a well-defined order. The results obtained with three different Reynolds and Cauchy numbers are compared with experimental data achieving good agreement. The considered range of Cauchy numbers represents three different types of canopies ranging from rigid up to highly flexible plants. The transient flow data and blade positions are statistically analyzed to gain deeper understanding of the complex physical processes for this kind of fluid structure interaction. For example, the correlation of role of large scale motion of the flexible blades in conjunction with coherent vortex structures of the flow is addressed. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlinear Flow Between Permeable Disks Using Computer-Extended Series Method

The problem of two-dimensional, steady, nonlinear flow of an incompressible, viscous fluid between two parallel permeable disks is studied using the computer-extended series solution (CESS). The limitation of the classical regular perturbation technique (RPT) in solving this problem is highlighted and the CESS method in conjunction with Padé approximation is advocated to analyze the problem for much larger values of suction/injection Reynolds number R and to achieve higher accuracy. The skin-friction coefficient and coefficient of pressure distribution are evaluated for different values of R . The advantages of using CESS method over the RPT and numerical technique are discussed.     

A defect correction approach to turbulence modeling

A method for resolving turbulent flow problems is presented, aiming at competing with the existing mathematical tractable Approximate Deconvolution Models in terms of accuracy, and outperforming these models in terms of the computational time needed. Full numerical analysis is performed, and the method is shown to be stable, easy to implement and parallelize, and computationally fast. The proposed method employs the defect correction approach to solve spatially filtered Navier–Stokes equations. A simple numerical test is provided that compares the method against the approximate deconvolution turbulence model (ADM). When resolving a fluid flow at high Reynolds number, the numerical example verifies the key feature of the method: while having the accuracy comparable to that of the ADM, the method computes in less than 80% of the time needed for the turbulence model—even before the parallelization.© 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 268–288, 2015     

微极液体在两个多孔圆盘间的MHD流动及其热传导

两个平行的无限大多孔圆盘,圆盘表面有均匀注入时,数值地研究圆盘间不可压缩导电微极流体,在横向外加磁场作用下的轴对称稳定层流.运用von Krmn的相似变换,将非线性运动的控制方程转化为无量纲形式.使用基于有限差分格式的算法,在相应的边界条件下,求解简化后耦合的常微分方程组.讨论Reynolds数、磁场参数、微极参数和Prandtl数,对流动速度和温度分布的影响.在特殊情况下,所得结果与已有文献的工作有着很好的一致性.研究表明,圆盘表面的传热率随着Rynolds数、磁场参数和Prandtl数的增加而增加;剪切应力随着注入的增加而减少,但它随着外部磁场的加强而增加.和Newton流体相比较,微极流体的剪切应力因素较弱,有利于聚合体加工过程中流动和温度的控制.     

Rimming flow of a power-law fluid: Qualitative analysis of the mathematical model and analytical solutions

Rimming flow of a non-Newtonian fluid on the inner surface of a horizontal rotating cylinder is investigated. Simple lubrication theory is applied since the Reynolds number is small and liquid film is thin. For the steady-state flow of a power-law fluid the mathematical model reduces to a simple algebraic equation regarding the thickness of the liquid film. The qualitative analysis of this equation is carried out and the existence of two possible solutions is rigorously proved. Based on this qualitative analysis, different regimes of the rimming flow are defined and analyzed analytically. For the particular case, when the flow index in a power-law constitutive equation is equal to 1/2, the problem reduces to the fourth order algebraic equation which is solved analytically by Ferrari method.     

Conforming Chebyshev Spectral Collocation Methods for the Solution of Laminar flow in a Constricted Channel

The numerical simulation of steady planar two-dimensional laminarflow of an incompressible fluid through an abruptly contractingchannel using spectral domain decomposition methods is described.The key features of the method are the decomposition of theflow region into a number of rectangular subregions and spectralapproximations that are pointwise C¹ continuous across subregioninterfaces. Spectral approximations to the solution are obtainedfor Reynolds numbers in the range [0, 500]. The size of thesalient corner vortex decreases as the Reynolds number increasesfrom 0 to around 45. As the Reynolds number is increased further,the vortex grows slowly. A vortex is detected downstream ofthe contraction at a Reynolds number of around 175 that continuesto grow as the Reynolds number is increased further.     

A combined analytical singularity subtraction method and compact implicit differencing scheme for aerodynamic mixing

In spite of the rapid advances in both scalar and parallel computational tools, the large number and breadth of variables involved in both design and inverse problems make the use of sophisticated fluid flow models impractical. With this restriction, it may be concluded that an important family of methods for mathematical/computational development are reduced or approximate models. In this study, a combined perturbation/numerical modeling methodology is developed. The numerical portion of the model uses a compact finite difference scheme, while analytical solutions are used to resolve singular behavior that is inherent to this flow. Solutions are presented to illustrate the efficiency of this methodology.     

A vortex method for fluid-particle systems

We consider a two-dimensional, dilute fluid-particle system with low Reynolds number for the flow around the particles and high Reynolds number for the bulk flow. We use a vortex method to calculate numerically the incompressible fluid phase. For the compressible particle phase we use a particle method and Voronoi diagrams to calculate the particle density. We use the Stokes-Oseen formula to represent approximately the force of the fluid on the particles. We give the results of a numerical experiment that show the effect of fluid particle interaction on the bulk flow.     

On dependence of dynamical structure of numerical solutions of fluid simulations on forcibly added randomness

In the present paper, the dependencies of the numerical results of fluid simulations on forcibly added randomness are discussed. The incompressible Navier-Stokes equations and the continuity equation are solved numerically by using the MAC (Maker-And-Cell) method and implicit temporal scheme. The model adopted in the present study is a flow around a two-dimensional circular cylinder and the Reynolds number is 1500. The randomness which is given by using the pseudo-random number is forcibly added in the time marching step of the discretized Navier-Stokes equations. Dependencies of the averaged structure of asymptotic numerical solutions on the randomness are discussed. Furthermore, the dependence of the qualitative structure of the asymptotic solution of each sample calculation on the amplitude of randomness is also studied. It is clarified that forcibly added random errors may cover the nonlinear errors which make the system unstable.