Implicit solution methods in computational fluid dynamics

A class of implicit finite difference schemes of the Beam and Warning approximate factorization type will be addressed. The development and analysis of various aspects of this class of schemes will be given along with the motivations behind many of the choices. Various acceleration and efficiency modifications such as matrix reduction, diagonalization and flux split schemes will be presented. The methods are demonstrated in fully vectorized codes for a CRAY type architecture. The emphasis will be on the Euler equations in generalized coordinates.     

Detailed computational and experimental fluid dynamics of fluidized beds

To describe the hydrodynamic phenomena prevailing in large industrial scale fluidized beds continuum models are required. The flow in these systems depends strongly on particle–particle interaction and gas–particle interaction. For this reason, proper closure relations for these two interactions are vital for reliable predictions on the basis of continuum models. Gas–particle interaction can be studied with the use of the lattice Boltzmann model (LBM), while the particle–particle interaction can suitably be studied with a discrete particle model. In this work it is shown that the discrete particle model, utilizing a LBM based drag model, has the capability to generate insight and eventually closure relations in processes such as mixing, segregation and homogeneous fluidization.     

Visualization of vortical flows in computational fluid dynamics

The concepts and methods of the visual representation of fluid dynamics computations of vortical flows are studied. Approaches to the visualization of vortical flows based on the use of various definitions of a vortex and various tests for its identification are discussed. Examples of the visual representation of solutions to some fluid dynamics problems related to the computation of vortical flows in jets, channels, and cavities and of the computation of separated flows occurring in flows around bodies of various shapes are discussed.     

Convenient system of FEM test functions for computational fluid dynamics

For the development of finite element schemes, a fundamentally new system of test functions defined on a finite element that is a convex quadrilateral is proposed. Due to the remarkable properties of the system (specifically, mutual orthogonality), the resulting matrices can be simplified and the corresponding construction procedures can be made more transparent, especially for problems in computational fluid dynamics. Thus, the system of test functions may play an important role in finite element methods as applied to two-dimensional problems.     

Analysis of performance of an iron-bath reactor using computational fluid dynamics

The performance of an iron-bath reactor has been studied using a comprehensive numerical model that combines a computational fluid dynamics approach for the gas phase and a heat and mass balance model for the bath. The model calculates:

• •coal, ore, flux and oxygen consumption;
• •post-combustion ratio (PCR);
• •heat-transfer efficiency (HTE);
• •off-gas temperature and composition;
• •heat transfer and chemical reactions between gas and iron and slag droplets; and
• •heat transfer between gas and bath, refractories and lance.

The model was validated with data reported by the Nippon Steel Corporation for a 100 t pilot plant, and the calculated and measured data are in good agreement. Modelling results showed that the dominant mechanisms of heat transfer from the gas to the bath are radiation to the slag surface and convection heat transfer to droplets.     

Inter-comparison and validation of computational fluid dynamics codes in two-stage meandering channel flows

This paper presents a study in the inter-comparison and validation of three-dimensional computational fluid dynamics codes which are currently used in river engineering. Finite volume codes PHOENICS, FLUENT and SSIIM; and finite element code TELEMAC3D are considered in this study. The work has been carried out by competent hydraulic modellers who are users of the codes and not involved in their development. This paper is therefore written from the perspective of independent practitioners of the techniques. In all codes, the flow calculations are performed by solving the three-dimensional continuity and Reynolds-averaged Navier–Stokes equations with the k–ε turbulence model. The application of each code was carried out independently and this led to slightly different, but nonetheless valid, models. This is particularly seen in the different boundary conditions which have been applied and which arise in part from differences in the modelling approaches and methodology adopted by the different research groups and in part from the different assumptions and formulations implemented in the different codes. Similar finite volume meshes are used in the simulations with PHOENICS, FLUENT and SSIIM while in TELEMAC3D, a triangular finite element mesh is used. The ASME Journal of Fluids Engineering editorial policy is taken as a minimum framework for the control of numerical accuracy. In all cases, grid convergence is demonstrated and conventional criteria, such as Y⁺, are satisfied. A rigorous inter-comparison of the codes is performed using large-scale experimental data from the UK Flood Channel Facility for a two-stage meandering channel. This example data set shows complex hydraulic behaviour without the additional complications found in natural rivers. Standardised methods are used to compare each model with the available experimental data. Results are shown for the streamwise and transverse velocities, secondary flow, turbulent kinetic energy, bed shear stress and free surface elevation. They demonstrate that the models produce similar results overall, although there are some differences in the predicted flow field and greater differences in turbulent kinetic energy and bed shear stress. This study is seen as an essential first step in the inter-comparison of some of the computational fluid dynamics codes used in the field of river engineering.     

Numerical simulation of scour around a submarine pipeline using computational fluid dynamics and discrete element method

Scour under a submarine pipeline can lead to structural failure; hence, a good understanding of the scour mechanism is paramount. Various numerical methods have been proposed to simulate scour, such as potential flow theory and single-phase and two-phase turbulent models. However, these numerical methods have limitations such as their reliance on calibrated empirical parameters and inability to provide detailed information. This paper investigates the use of a coupled computational fluid dynamics-discrete element method (CFD-DEM) model to simulate scour around a pipeline. The novelty of this work is to use CFD-DEM to extract detailed information, leading to new findings that enhance the current understanding of the underlying mechanisms of the scour process. The simulated scour evolution and bed profile are found to be in good agreement with published experimental results. Detailed results include the contours of the fluid velocity and fluid pressure, particle motion and velocity, fluid forces on the particles, and inter-particle forces. The sediment transport rate is calculated using the velocity of each single particle. The quantitative analysis of the bed load layer is also presented. The numerical results reveal three scour stages: onset of scour, tunnel erosion, and lee-wake erosion. Particle velocity and force distributions show that during the tunnel erosion stage, the particle motion and particle–particle interactive forces are particularly intense, suggesting that single-phase models, which are unable to account for inter-particle interactions, may be inadequate. The fluid pressure contours show a distinct pressure gradient. The pressure gradient force is calculated and found to be comparable with the drag force for the onset of scour and the tunnel erosion. However, for the lee-wake erosion, the drag force is shown to be the dominant mechanism for particle movements.     

Preconditioning for boundary control problems in incompressible fluid dynamics

PDE‐constrained optimization problems arise in many physical applications, prominently in incompressible fluid dynamics. In recent research, efficient solvers for optimization problems governed by the Stokes and Navier–Stokes equations have been developed, which are mostly designed for distributed control. Our work closes a gap by showing the effectiveness of an appropriately modified preconditioner to the case of Stokes boundary control. We also discuss the applicability of an analogous preconditioner for Navier–Stokes boundary control and provide some numerical results.     

Determination of open boundary conditions for computational fluid dynamics (CFD) from interior observations

An optimization approach for the determination of open boundary conditions for Computational Fluid Dynamics is introduced, whereas the error between the solution σ and interior observations ω is minimized. The numerical weather prediction (NWP) model ALADIN–Austria provides data of wind speed and wind direction at virtual weather stations within the area of interest. Also, data from real weather stations and other sources can be incorporated into the model, respectively. In this work, the optimization method is applied to the constant density Navier–Stokes Equations. Thereby, for stabilizing the ill-posed pseudo inverse problem several regularization methods are reviewed. Further, numerical studies are carried out to identify the supreme regularization method for the presented application. Finally, the algorithm is applied to the micro- and meso-scale flow over the Grimming mountain, Austria. The results are compared with real weather station data and show suitable correlation with the measurements.     

Computational fluid dynamics based dynamic modeling of parafoil system

The calculation of aerodynamic coefficients has been one of the key issues when modeling parafoil systems, that directly affects model precision. This study relates to investigate limitations of traditional calculation methods. As a result, we achieve aerodynamic parameters of a parafoil using computational fluid dynamics simulations. Also we employ the least square method as a tool for the rapid identification of deflection factors of aerodynamic coefficients. The estimated aerodynamic coefficients of the system were incorporated into the dynamic equations of the parafoil to implement a six degree of freedom model of a parafoil system according to the Kirchhoff equations. Numerical results generated by simulation and airdrop testing demonstrate that the established model can accurately describe the flight characteristics of the parafoil system.     

A computational model of a transcritical R744 ejector based on a homogeneous real fluid approach

A mathematical model of the compressible transonic single- and two-phase flow of a real fluid is discussed in this paper. The model was originally developed to simulate a refrigerant flow through a heat pump ejector. In the proposed approach, a temperature-based energy equation is replaced with an enthalpy-based formulation, in which the specific enthalpy, instead of the temperature, is an independent variable. A thermodynamic and mechanical equilibrium between gaseous and liquid phases is assumed for the two-phase flow. Consequently, real fluid properties, such as the density, the dynamic viscosity and the diffusion coefficient, are defined as functions of the pressure and the specific enthalpy. The energy equation formulation is implemented in commercial CFD software using subroutines that were developed in-house. The formulations was tested extensively for a single-phase flow of the R141b refrigerant, and for a two-phase flow of the R744 fluid (carbon dioxide) that occurred in a 3-D model of the ejector motive nozzle. In the model validation procedure, a satisfactory comparison between the experimental and computational results of the primary and secondary mass flow rates was obtained for both flow regimes. In addition, in the case of the R744 flow, the pressure distribution along the centre line of the ejector was accurately predicted as well. Furthermore, the results also shows that geometry modelling and measurement accuracy play an important in the final numerical results. As a result of the reasonable computational times, this method can be effectively used for the design of ejectors and also in geometric optimisation computations.     

Arterial dynamics based on the model of a multilayered shell with fluid flow

The dynamic process in a blood vessel segment of finite length is investigated. The vessel is assumed to be a multilayer cylindrical shell consisting of a large number of alternating layers, each of which possesses anisotropic elastic properties. Geometric nonlinearity is taken into account. The blood is assumed to be an ideal compressible fluid. A numerical solution has been obtained using a computer.     

Investigation of supercomputer capabilities for the scalable numerical simulation of computational fluid dynamics problems in industrial applications

Two main issues of the efficient usage of computational fluid dynamics (CFD) in industrial applications—simulation of turbulence and speedup of computations—are analyzed. Results of the investigation of potentials of the eddy-resolving approaches to turbulence simulation in industrial applications with the use of arbitrary unstructured grids are presented. Algorithms for speeding up the scalable high-performance computations based on multigrid technologies are proposed.     

Equation-Free multiscale computational analysis of individual-based epidemic dynamics on networks

The surveillance, analysis and ultimately the efficient long-term prediction and control of epidemic dynamics appear to be some of the major challenges nowadays. Detailed individual-based mathematical models on complex networks play an important role towards this aim. In this work, it is shown how one can exploit the Equation-Free approach and optimization methods such as Simulated Annealing to bridge detailed individual-based epidemic models with coarse-grained, system-level analysis within a pair-wise representation perspective. The proposed computational methodology provides a systematic approach for analyzing the parametric behavior of complex/multiscale epidemic simulators much more efficiently than simply simulating forward in time. It is shown how steady state and (if required) time-dependent computations, stability computations, as well as continuation and numerical bifurcation analysis can be performed in a straightforward manner. The approach is illustrated through a simple individual-based SIRS epidemic model deploying on a random regular connected graph. Using the individual-based simulator as a black box coarse-grained timestepper and with the aid of Simulated Annealing I compute the coarse-grained equilibrium bifurcation diagram and analyze the stability of the stationary states sidestepping the necessity of obtaining explicit closures at the macroscopic level.     

Comparisons of two commercial computational fluid dynamics codes in modelling pulverised coal combustion for a 2.5 MW burner

This paper reports an investigation into the performance of two commercial computational fluid dynamics (CFD) codes for pulverised coal combustion prediction. The two codes employed were FLUENT and FLOW3D 3.2 (now called CFX). The experimental case considered was a 2.5 MW Aerodynamically Air Staged Burner (AASB) fired in isolation into a rectangular furnace. Predictions were compared to velocity, temperature and species concentration experimental data. Some slight differences were noted between the two CFD codes predictions beyond one burner diameter downstream of the burner exit. Discrepancies between the predictions of the two CFD codes were concluded to be due to differences in the physical models used to describe devolatilisation and gaseous combustion. This paper therefore concludes that, for this case, the two commercial CFD codes were capable of predicting good `trend' answers.     

Numerical simulation of dense fluid-particle flows using computational fluid dynamics (CFD) and discrete element method (DEM)

Discrete Element Method (DEM) has been successfully coupled with Computational Fluid Dynamics (CFD) in the framework of OpenFOAM an open source CFD simulation code. In the current study, at first the model is validated with the simple test case of spherical particle comparing the results with the analytical solution. Then the simulation of a gaseous fluidized bed is considered. The coupled mass and momentum balance equations are used to calculate the flow behavior, particle fluidization and bubble formation. The dimensions of the simulation domain are similar to Link et al. (2005) but with different stiffness of particles. The higher velocity of gaseous fluid relative to particles entering through a jet causes the particles to fluidize. The particles behavior, fluidization, bubble formation and the velocity vectors of particles show a good agreement with the literature. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A computational approach for understanding immune response to multiple epitopes based on optimal control formulation

The immune system does not response in equal probability to every epitope of an invader. We investigate the immune system’s decision making process using optimal control principles. Mathematically, this formulation requires the solution of a two-point boundary-value problem, which is a challenging task especially when the control variables are bounded. In this work, we develop a computational approach based on the shooting technique for bounded optimal control problems. We then utilize the computational approach to carry out extensive numerical studies on a simple immune response model of two competing controls. Numerical solutions demonstrate that the results of optimal control depend on the objective function, the limitations on control inputs, as well as the amounts of peptides. Moreover, the state space of peptides can be divided into different regions according the properties of the solutions. The developed algorithm not only provides a useful tool for understanding decision making strategies of the immune system but can also be utilized to solve other complex optimal control problems.     

Hamiltonian differencing of fluid dynamics

By analyzing the Hamiltonian structures of several representations of continuous Lagrangian fluid dynamics, a universal Hamiltonian form is developed which unifies those structures and applies both to the continuous and spatially discrete cases. Then the universal Hamiltonian form is used as a “template” for generating numerical differencing schemes which retain the underlying Hamiltonian structure of the continuous theory. Examples are discussed of these spatial differencing schemes for the Euler equations in one, two, and three dimensions. In one dimension, the nondissipative part of the von Neumann-Richtmeyer scheme is recovered as a special case.