Simulation Of Two-dimensional Flow Research Articles

Computer simulation of two-dimensional electrolyte flow in electrochemical machining

A mathematical model and a method for numerical modeling of two-dimensional electrolyte flow in the interelectrode gap during electrochemical machining (ECM) are presented. Programs for modeling electrolyte flow and observing the distribution of ECM parameters are designed. The modeling results are compared with experimental data on continuous ECM and ECM with a vibrating tool.

Evaluation of the Lagrangian particle dispersion model DIPCOT against data from wind tunnel simulations of quasi two-dimensional turbulent flow

The stochastic dispersion model DIPCOT was validated against data from wind tunnel experiments where heat, used as the tracer, was released in a quasi two-dimensional turbulent flow. Dispersion simulations, based on Langevin equation, were performed using measurements and the model predictions were quantitatively compared to the experimental data. Two approaches of the drift term in Langevin equation were examined, utilising the first three and the first four moments of turbulent velocity, respectively. The overall behaviour of the model is quite satisfactory. The form of the drift term affected the predictions; the introduction of the fourth moment resulted in better estimations of the maximum concentrations. However, the mean performance of the model remained stable, irrespective of the drift term formulation.

623 血流の粒子法シミュレーション(赤血球が与える血流への影響)(S02 粒子法による先端シミュレーション)

A two-dimensional computer simulation of blood flow between parallel plates was carried out using particle method to investigate effects of red blood cells (RBCs) on blood flow properties. The RBCs and plasma were discretized by the particles that have the characteristics of the elastic membrane and the viscous incompressible fluid, respectively. The simulation results demonstrated that apparent blood flow resistance was affected by hematocrit (HCT) that controlled degree of deformation of RBCs. The lower HCT led to the lower resistance because the RBCs were more concentrated in the center of flow channel due to their larger deformation.

E106 粒子法を用いた血流の直接シミュレーション

A particle method for computer simulation of blood flow is proposed to directly analyze the characteristic mechanical behavior of red blood cells (RBCs) in blood flow. The entire simulation region including plasma and an RBC was discretized by particles that move in Lagrangian coordinates. The MPS method was applied to the incompressible flow analysis of plasma, and an elastic spring model based on the minimum energy principle to the motion of deformable RBC. A two-dimensional simulation of blood flow between parallel plates revealed that the proposed method successfully expressed the deformation of RBC depending on membrane stiffness during its movement downstream, corresponding to a deformation in a parachute shape observed in experiments.

B202 LES乱流解析結果のウェーブレット分析

Large eddy simulation of two-dimensional isotropic turbulent flow is performed using dynamic SGS model under assumption of local interscale equilibrium. The numerical results show that the dynamic SGS model can appropriately evaluate the reverse cascade of energy, which is a major characteristic of two-dimensional turbulence.

Simplified models for predicting the onset of liquid water droplet instability at the gas diffusion layer/gas flow channel interface

Simplified models that are based on macroscopic force balances and droplet-geometry approximations are presented for predicting the onset of instability leading to removal of water droplets at the gas diffusion layer (GDL)/gas flow channel (GFC) interface. Visualization experiments are carried out to observe the formation, growth, and removal or instability of the water droplets at the GDL/GFC interface of a simulated polymer electrolyte fuel cell cathode. Droplet-instability diagrams or ‘windows’ computed by the simplified models are compared with those measured experimentally, and good agreement is obtained. Two-dimensional flow simulations employing the finite element method coupled with an arbitrary Lagrangian–Eulerian formulation for determining the liquid/gas interface position are also performed to assess the simplified cylindrical-droplet model. Necessary conditions for preventing fully grown droplets from lodging in the flow channel are derived using the simplified models. It is found that droplet removal can be enhanced by increasing flow channel length or mean gas flow velocity, decreasing channel height or contact angle hysteresis, or making the GDL/GFC interface more hydrophobic. Copyright © 2005 John Wiley & Sons, Ltd.

Mechanisms of Up-Valley Winds

Abstract The basic physical mechanisms governing the daytime evolution of up-valley winds in mountain valleys are investigated using a series of numerical simulations of thermally driven flow over idealized three-dimensional topography. The three-dimensional topography used in this study is composed of two, two-dimensional topographies: one a slope connecting a plain with a plateau and the other a valley with a horizontal floor. The present two-dimensional simulations of the valley flow agree with results of previous investigations in that the heated sidewalls produce upslope flows that require a compensating subsidence in the valley core bringing down potentially warmer air from the stable free atmosphere. In the context of the three-dimensional valley–plain simulations, the authors find that this subsidence heating in the valley core is the main contributor to the valley– plain temperature contrast, which, under the hydrostatic approximation, is the main contributor to the valley– plain pressure difference that drives the up-valley wind.

Effect of leading edge cut on the aerodynamics of ram‐air parachutes

AbstractThe effect of the configuration of leading edge cut on the aerodynamic performance of ram‐air parachutes is studied via two‐dimensional flow simulations. The incompressible Reynolds‐averaged Navier–Stokes equations, in primitive variables, are solved using a stabilized finite‐element formulation. The Baldwin–Lomax model is employed for turbulence closure. Flow past an LS(1) 0417 airfoil is investigated for various configurations of the leading edge cut and results are compared with those from a Clark‐Y airfoil section. It is found that the configuration of the leading edge cut affects the lift‐to‐drag ratio (L/D) of the parachute very significantly. The L/D value has strong implications on the flight performance of the parachute. One particular configuration results in a L/D value that is in excess of 25 at 7.5° angle of attack. Results are presented for other angles of attack for this configuration. Copyright © 2004 John Wiley & Sons, Ltd.

Acceleration of steady-state lattice Boltzmann simulations on non-uniform mesh using local time step method

In this paper, the local time step method is applied to the lattice Boltzmann method (LBM) on non-uniform grid (generalized form of interpolation supplemented LBM: GILBM) for steady flow simulations. The local time step method is known to be an effective technique to accelerate the solution to the converged steady state on non-uniform grid. First, code validation for global time step method is performed by solving flow around a cylinder at low Reynolds numbers. Our results show good agreement with previous studies. Two-dimensional flow simulations around an airfoil were performed in order to validate the code using the local time step method and the results are compared with the global time step solutions. The pressure distribution and the aerodynamic coefficients of global and local time step results are in good agreement. They are also consistent with the previous studies. At the same time, CPU time required to obtain the steady-state solutions using the local time step are reduced by 70–80% compared with that using global time step.

Implicit space–time residual distribution method for unsteady laminar viscous flow

The class of multidimensional upwind residual distribution (RD) schemes has been developed in the past decades as an attractive alternative to the finite volume (FV) and finite element (FE) approaches. Although they have shown superior performances in the simulation of steady two-dimensional and three-dimensional inviscid and viscous flows, their extension to the simulation of unsteady flow fields is still a topic of intense research [ICCFD2, International Conference on Computational Fluid Dynamics 2, Sydney, Australia, 15–19 July 2002; M. Mezine, R. Abgrall, Upwind multidimensional residual schemes for steady and unsteady flows]. Recently the space–time RD approach has been developed by several researchers [Int. J. Numer. Methods Fluids 40 (2002) 573; J. Comput. Phys. 188 (2003) 16; Á.G. Csı́k, Upwind residual distribution schemes for general hyperbolic conservation laws and application to ideal magnetohydrodynamics, PhD thesis, Katholieke Universiteit Leuven, 2002; J. Comput. Phys. 188 (2003) 16; R. Abgrall; M. Mezine, Construction of second order accurate monotone and stable residual distribution schemes for unsteady flow problems] which allows to perform second order accurate unsteady inviscid computations. In this paper we follow the work done in [Int. J. Numer. Methods Fluids 40 (2002) 573; Á.G. Csı́k, Upwind residual distribution schemes for general hyperbolic conservation laws and application to ideal magnetohydrodynamics, PhD thesis, Katholieke Universiteit Leuven, 2002]. In this approach the space–time domain is discretized and solved as a ( d+1)-dimensional problem, where d is the number of space dimensions. In [Int. J. Numer. Methods Fluids 40 (2002) 573; Á.G. Csı́k, Upwind residual distribution schemes for general hyperbolic conservation laws and application to ideal magnetohydrodynamics, PhD thesis, Katholieke Universiteit Leuven, 2002] it is shown that thanks to the multidimensional upwinding of the RD method, the solution of the unsteady problem can be decoupled into sub-problems on space–time slabs composed of simplicial elements, allowing to obtain a true time marching procedure. Moreover, the method is implicit and unconditionally stable for arbitrary large time-steps if positive RD schemes are employed. We present further development of the space–time approach of [Int. J. Numer. Methods Fluids 40 (2002) 573; Á.G. Csı́k, Upwind residual distribution schemes for general hyperbolic conservation laws and application to ideal magnetohydrodynamics, PhD thesis, Katholieke Universiteit Leuven, 2002] by extending it to laminar viscous flow computations. A Petrov–Galerkin treatment of the viscous terms [Project Report 2002-06, von Karman Institute for Fluid Dynamics, Belgium, 2002; J. Dobeš, Implicit space–time method for laminar viscous flow], consistent with the space–time formulation has been investigated, implemented and tested. Second order accuracy in both space and time was observed on unstructured triangulation of the spatial domain. The solution is obtained at each time-step by solving an implicit non-linear system of equations. Here, following [Int. J. Numer. Methods Fluids 40 (2002) 573; Á.G. Csı́k, Upwind residual distribution schemes for general hyperbolic conservation laws and application to ideal magnetohydrodynamics, PhD thesis, Katholieke Universiteit Leuven, 2002], we formulate the solution of this system as a steady state problem in a pseudo-time variable. We discuss the efficiency of an explicit Euler forward pseudo-time integrator compared to the implicit Euler. When applied to viscous computation, the implicit method has shown speed-ups of more than a factor 50 in terms of computational time.

Lattice Boltzmann simulation of the flow interference in bluff body wakes

This paper presents a two-dimensional numerical simulation of fluid flow around a couple of identical circular cylinders aligned, respectively, along and orthogonal to the main-flow direction, at several distances. A lattice Boltzmann (LB) method is used. The forces resulting from fluid–solid interaction are calculated by considering the momentum exchanged between the fluid and the solid surfaces. Bluff body wake interference and its effect on drag and lift forces is studied in detail. The drag and the lift coefficients are obtained and compared with other existing results. A transition regime is obtained when the cylinders are aligned orthogonal to the main-flow direction and separated by distances smaller than about 2D.

Lattice Boltzmann simulation of the flow interference in bluff body wakes

This paper presents a two-dimensional numerical simulation of fluid flow around a couple of identical circular cylinders aligned, respectively, along and orthogonal to the main-flow direction, at several distances. A lattice Boltzmann (LB) method is used. The forces resulting from fluid–solid interaction are calculated by considering the momentum exchanged between the fluid and the solid surfaces. Bluff body wake interference and its effect on drag and lift forces is studied in detail. The drag and the lift coefficients are obtained and compared with other existing results. A transition regime is obtained when the cylinders are aligned orthogonal to the main-flow direction and separated by distances smaller than about 2D.

Simulation of two‐dimensional turbulent flows in a rotating annulus

AbstractRotating water tank experiments have been used to study fundamental processes of atmospheric and geophysical turbulence in a controlled laboratory setting. When these tanks are undergoing strong rotation the forced turbulent flow becomes highly two dimensional along the axis of rotation. An efficient numerical method has been developed for simulating the forced quasi‐geostrophic equations in an annular geometry to model current laboratory experiments. The algorithm employs a spectral method with Fourier series and Chebyshev polynomials as basis functions. The algorithm has been implemented on a parallel architecture to allow modelling of a wide range of spatial scales over long integration times. This paper describes the derivation of the model equations, numerical method, testing and performance of the algorithm. Results provide reasonable agreement with the experimental data, indicating that such computations can be used as a predictive tool to design future experiments. Copyright © 2004 John Wiley & Sons, Ltd.

Experimental and numerical investigation of confined unsteady supersonic flow over cavities

AbstractExperimental investigations were carried out to study the acoustic radiation from a rectangular wall mounted cavity in a confined supersonic flow. The free-stream Mach number was maintained at 1·5 and the cavity length-to-depth ratio was varied from 0·43 to 5·0. Acoustic measurements made on the top wall show jumps in the dominant frequency as the cavity behaviour changes from shallow-to-square-to-deep cavity. Numerical simulations of this unsteady two-dimensional flow using the commercially available software FLUENT have also been carried out. Unsteady pressure data at the same location in the flow field as the pressure transducers in the experiments was collected. FFT analysis of the unsteady pressure data was performed to obtain the dominant acoustic frequencies. The values for these dominant frequencies predicted by the numerical calculations agree well with experimental data. The numerical study also predicts the frequency jump observed in experiments.

Central scheme for two-dimensional dam-break flow simulation

A new second-order central scheme (KT), proposed by Kurganov and Tadmor, have been used for the solution of the two-dimensional dam-break problem. After having assumed as basis of the dam-break phenomenon the set of 2D nonhomogeneous Saint–Venant equations, the KT scheme in its semi-discrete second-order form has been extended for taking into account the presence of a source term. Time integration has been performed by using a third-order TVD Runge–Kutta scheme. To demonstrate the accuracy of this explicit method, the solution obtained by this model for a dam-break problem of one-dimensional flow has been compared with the corresponding analytical solution, moreover, the solutions obtained for two test cases of two-dimensional flow have been compared with the experimental results.

Two-dimensional simulation of water flow and solute transport below furrows: model calibration and validation

In this study a two-dimensional numerical flow/transport model (HYDRUS-2D) was calibrated and experimentally validated using data from long furrow irrigation experiments. The model was calibrated using data from an experiment carried out assuming free-draining (FD) outlet conditions, and subsequently validated against data from three experiments assuming blocked-end conditions. The data were analyzed using the Richards' equation for variably saturated flow and either the traditional convection–dispersion equation (CDE) or the physical nonequilibrium mobile–immobile (MIM) model for solute transport. Optimization was accomplished by means of Levenberg–Marquardt optimization in combination with the HYDRUS-2D model. Simultaneous and two-step optimization approaches were used to estimate the soil hydraulic and solute transport parameters near the FD furrow inlet and outlet sites. First, the saturated hydraulic conductivity ( K s) and CDE or MIM solute transport parameters were estimated simultaneously. We also used sequential (two-step) estimation in which we first estimated the soil hydraulic parameters followed by estimation of the solute transport parameters. In the two-step method, the saturated soil water content ( θ s), the n parameter in van Genuchten's soil water retention model, and K s values were estimated during the first step, and the CDE or MIM solute transport parameters during the second step. Estimated soil hydraulic and solute transport parameters were found to vary substantially between the inlet and outlet sites. Estimated CDE and MIM transport parameters were very similar for both optimization approaches. The two-step method significantly improved predictions of the soil water content during model calibration, while the solute concentration predictions were nearly the same for both approaches, with both not providing a good description of the observed concentrations. Solute data were also analyzed using horizontal averages to somewhat lessen the effects of spatial variability. Horizontally averaged concentration distributions showed better agreement with the predictions. Soil water contents for the three blocked-end experiments during model validation were well predicted. The two-step method produced slightly better agreement with observed data. However, both optimization approaches produced relatively poor agreement between measured and predicted solute concentrations and deep percolation rates.

A winwin mechanism for low-drag transients in controlled two-dimensional channel flow and its implications for sustained drag reduction

A simple pressure-based feedback control strategy for wall-transpiration control of incompressible unsteady two-dimensional channel flow was recently investigated by Aamo, Krstic & Bewley (2003). Nonlinear two-dimensional channel flow simulations which implemented this control strategy resulted in flow transients with instantaneous drag far lower than that of the corresponding laminar flow. The present article examines the physical mechanism by which this very low level of instantaneous drag was attained. It then explores the possibility of achieving sustained drag reductions to below the laminar level by initiating such low-drag transients on a periodic basis. All attempts at sustaining the mean flow drag below the laminar level fail, perhaps providing indirect evidence in favour of the conjecture that the laminar state might provide a fundamental ‘performance limitation’ in such flows. Mathematical analysis of two-dimensional and three-dimensional channel-flow systems establishes a direct link between the average drag increase due to flow-field unsteadiness and a weighted space/time average of the Reynolds stress. Phenomenological justification of the conjecture is provided by a Reynolds analogy between convective momentum transport and convective heat transport. Proof of the conjecture remains an open problem.

Flutter, Tumble and Vortex Induced Autorotation

The phenomenon of flutter and tumble of objects in free fall has been studied using two-dimensional numerical simulations of uniform flow past a plate which is free to rotate about a fixed axis through its centroid. Particular focus is on the effect of Reynolds number and plate thickness-to-length ratio on the flutter-to-tumble transition and on the observed frequency of the angular motions. Simulations indicate that the tendency to tumble increases with increasing Reynolds number and decreasing thickness ratio. A case is also made that the tumbling frequency for two-dimensional plates is governed by a Karman type vortex shedding process. These results for this pinned plate have also been verified by simulating a limited number of free-fall cases.

Two-Dimensional Finite Element Simulation of Material Flow in the Friction Stir Welding Process

Solid mechanics based finite element models and computational procedures have been developed by the authors to study and simulate the friction stir welding process. In this paper, two-dimensional simulation results of the material flow pattern and spatial velocity field around the rotating tool pin during welding, and the positions of material particles around the pin after welding, are presented. Material flow pattern predictions are found to compare favorably with experimental observations. Simulation results suggest that material particles in front of the tool pin tend to pass and get behind the rotating pin from the retreating side of the pin. Similarities between predicted velocity fields based on two different tool-workpiece interface models are described in detail, and implications of these findings (e.g., to fluid dynamics based models) are discussed.

1310 Dual-Bell Nozzle 形状が比推力に及ぼす影響に関する数値解析による研究(GS-1.5 流れの数値解析(2))

In dual-bell nozzles, the specific impulse is decreased near the transition between two operation modes. In this paper, two-dimensional axisymmetric flow simulations are performed to understand the cause of the decrease of specific impulse and to propose a method to minimize the decrease. It was found that the specific impulse during start up transient could be increased by providing a step at the inflection point of the nozzle geometry.