Flows In Complicated Geometries Research Articles

A Combined Experimental and Numerical Analysis on the Aerodynamics of a Carbon-Ceramic Brake Disc

<div>Composite ceramic brake discs are made of ceramic material reinforced with carbon fibers and offer exceptional advantages that translate directly into higher vehicle performance. In the case of an electric vehicle, it could increase the range of the vehicle, and in the case of conventional internal combustion engine vehicles, it means lower fuel consumption (and consequently lower CO<sub>2</sub> emissions). These discs are typically characterized by complex internal geometries, further complicated by the presence of drilling holes on both friction surfaces. To estimate the aerothermal performance of these discs, and for the thermal management of the vehicle, a reliable model for predicting the air flowing across the disc channels is needed. In this study, a real carbon-ceramic brake disc with drilling holes was investigated in a dedicated test rig simulating the wheel corner flow conditions experimentally using the particle image velocimetry technique and numerically. The simulation was performed using the moving reference frame (MRF) approach and the experimental data were used to validate the numerical model. The results show that drilling holes contribute to about 13% of the inlet mass flow and more than 86% of the air driven into the brake disc comes from the main inlet of the disc. Moreover, the numerical results are in an agreement with experimental data, supporting MRF approach as a suitable model for the analysis of complex flows in complicated geometries.</div>

Elastoviscoplastic rheology and aging in a simplified soft glassy constitutive model

Yield stress fluids display a rich rheological phenomenology. Beyond the defining existence of a yield stress in the steady state flow curve, this includes in many materials rather flat viscoelastic spectra over many decades of frequency in small amplitude oscillatory shear; slow stress relaxation following the sudden imposition of a small shear strain; stress overshoot in shear startup; logarithmic or sublinear power law creep following the imposition of a shear stress below the yield stress; creep followed by yielding after the imposition of a shear stress above the yield stress; richly featured Lissajous-Bowditch curves in large amplitude oscillatory shear; a Bauschinger effect, in which a material's effective yield strain is lowered under straining in one direction, following a preceding strain in the opposite direction; hysteresis in up-down shear rate sweeps; and (in some materials) thixotropy and/or rheological ageing. A key challenge is to develop a constitutive model that contains enough underlying mesoscopic physics to have meaningful predictive power for the full gamut of rheological behaviour just described, with only a small number of model parameters, and yet is simple enough for use in computational fluid dynamics to predict flows in complicated geometries, or complicated flows that arise due to spontaneous symmetry breaking instabilities even in simple geometries. Here we introduce such a model, motivated by the widely used soft glassy rheology model, and show that it captures all the above rheological features.

Numerical Simulation of High Mach Number Flow using the Finite Difference Lattice Boltzmann Method (FDLBM)

The Lattice Boltzmann Method (LBM) is known as a powerful numerical tool to simulate fluid flow problems. Particularly, it has shown a unified strength for solving incompressible fluid flows in complicated geometries. Many researchers have used Lattice Boltzmann (LB) concept to simulate compressible flows, but the common defect of most of previous models is the stability problem at high Mach number fluid flows. In this paper we introduce a FLDBM-model, which is capable to simulate fluid flows with any specific heat ratios and higher Mach numbers, from 0 to 30 or higher. Compressibility is applied using multiple particle speeds in a thermal fluid. Based on the discrete-velocity-model, a new finite difference method and an artificial viscosity are implemented, which must find a balance between numerical stability and accuracy of simulation. The introduced model is checked and validated again well-known benchmark tests such as one dimensional shock tubes, supersonic bump and ramp (two dimensional). Both sets of results have a reasonable agreement regarding to exact solutions.

Two-phase flow in complicated geometries

We study modeling two-phase flow in complicated geometries. We use modern mesh generation techniques to improve the quality of the mesh and at the same time both reduce the number of elements and capture the geometry accurately. The generated meshes consist of orthogonally optimized general hexahedras. To model the flow in general hexahedras, we use the multipoint flux mixed finite element method. As a test problem we use the Frio experiment data.

DEVELOPMENT AND PRELIMINARY ASSESSMENT OF A THREE-DIMENSIONAL THERMAL HYDRAULICS CODE, CUPID

For the analysis of transient two-phase flows in nuclear reactor components, a three-dimensional thermal hydraulics code, named CUPID, has been developed. The CUPID code adopts a two-fluid, three-field model for two-phase flows, and the governing equations were solved over unstructured grids, which are very useful for the analysis of flows in complicated geometries. To obtain numerical solutions, the semi-implicit numerical method for the REALP5 code was modified for an application to unstructured grids, and it has been further improved for enhanced accuracy and fast running. For the verification of the CUPID code, a set of conceptual problems and experiments were simulated. This paper presents the flow model, the numerical solution method, and the results of the preliminary assessment.

Steam condensing flow modeling in turbine channels

The numerical method for modeling of the transonic steam flows with homogeneous and/or heterogeneous condensation has been presented. The experiments carried out for the Laval nozzles, for 2-D turbine cascades and for a 3-D flow in real turbine were selected to validate an in-house CFD code adjusted to the calculations of the steam condensing flows in complicated geometries. The sensitivity of the condensation model and difficulties in the validation process of the CFD code have been discussed. These difficulties limit the possibilities of verification and improvement of the condensation theory based on the existing experimental data. The numerical simulations were based on the time-dependent 3-D Reynolds averaged Navier–Stokes (RANS) equations coupled with two-equations turbulence model ( k–ω SST) and additional conservation equations for the liquid phase. The set of governing equations has been closed by a ‘local’ real gas equation of state. The condensation phenomena were modeled on the basis of the classical nucleation theory. The heterogeneous condensation model on the insoluble as well as soluble impurities was implemented into presented CFD code. The system of governing equations was solved by means of a finite volume method on a multi-block structural grid.

Numerical Simulation of Electroosmotic Flow

We have developed a numerical scheme to simulate electroosmotic flows in complicated geometries. We studied the electroosmotic injection characteristics of a cross-channel device for capillary electrophoresis. We found that the desired rectangular shape of the sample plug at the intersection of the cross-channel can be obtained when the injection is carried out at high electric field intensities. The shape of the sample plug can also be controlled by applying an electric potential or a pressure at the side reservoirs. Flow induced from the side channels into the injection channel squeezes the streamlines at the intersection, thus giving a less distorted sample plug. Results of our simulations agree qualitatively with experimental observations.

Invariant discretization of the k-ϵ model in general co-ordinates for prediction of turbulent flow in complicated geometries

An invariant formulation and finite volume discretization of the standard k-ϵ turbulence model in general curvilinear co-ordinates is presented. The k-ϵ model is implemented together with the incompressible Navier-Stokes equations on staggered grids with contravariant flux components as unknowns. A proof that k and ϵ are non-negative is given. Positive schemes in the implementation of the k-ϵ model are evaluated. Discretization of boundary conditions is considered. The numerical method is applied to a turbulent flow across a staggered tube bank.

Time Accurate Solution of Unsteady Viscous Flow Problems using the Finite-Element Method. 1st Report. Numerical Scheme.

A new finite-element method is proposed for solving unsteady incompressible Navier Stokes equations. The basis of the method is to shift the governing equations to the upstream direction by a distance proportional to the local flow velocity multiplied by the time increment. The method thus differs from most conventional upwind formulations which shift the governing equations based on the element dimension. The proposed method guarantees reasonable stability for simulations of high Reynolds number flows without introducing excessive numerical diffusion which is often encountered with conventional upwind methods. The accuracy of the proposed upwind method is first demonstrated for a simple advection-diffusion problem known as 'rotating cone'. Several simulations of unsteady laminar flows are then performed to test the full Navier-Stokes formulation. The simulated results show good agreement with the experimental data. Hence, the proposed method seems quite promising for simulations of unsteady flows in complicated geometries.

An implicit, bidiagonal numerical method for solving the Navier-Stokes equations

In recent years, much progress has been made in solving fluid dynamical problems using finite difference methods. Solving inviscid compressible problems in two and three dimensions has become almost routine with many suitable methods, explicit or implicit, available. The problem of compressible, viscous flows in complicated geometries remains, however, a major challenge. Here fine mesh spacing in the viscous flow regions makes the explicit methods with their simple boundary conditions extremely costly. Existing implicit methods can make use of large time steps, but require inversions of large block tridiagonal matrices. A method recently developed by MacCormack eliminates this disadvantage by introducing a predictor-corrector scheme requiring the inversion of only block bidiagonal matrices. It is the aim of present work to extend this method to allow solution of viscous, compressible problems in general coordinates for arbitrary two-dimensional geometries.

Non-Newtonian Flow through Porous Media. I. Theoretical

A method is suggested for characterizing viscoelastic fluids in an approximate but useful way for the description of flow in complicated geometries. This method rests on the determination of a zero-shear limiting viscosity, a characteristic time, and a dimensionless parameter relating to the slope of a log-log plot of viscosity vs. shear rate in the “power law” region. It is then shown how such parameters can be used in correlating experimental data on pressure drops through packed beds at constant volumetric flow rate. This is done by a combination of a porous medium model calculation and dimensional analysis. It is shown how the characteristic time of the fluid can be used to designate regions of behavior where elastic effects are important.