A. D. Gosman

Solution of the implicitly discretised reacting flow equations by operator-splitting

Abstract A non-iterative method for handling the coupling of the implicitly discretised time-dependent fluid flow equations is described. The method is based on the use of pressure and velocity as dependent variables and is hence applicable to both the compressible and incompressible versions of the transport equations. The main feature of the technique is the splitting of the solution process into a series of steps whereby operations on pressure are decoupled from those on velocity at each step, with the split sets of equations being amenable to solution by standard techniques. At each time-step, the procedure yields solutions which approximate the exact solution of the difference equations. The accuracy of this splitting procedure is assessed for a linearised form of the discretised equations, and the analysis indicates that the solution yielded by it differs from the exact solution of the difference equations by terms proportional to the powers of the time-step size. By virtue of this, it is possible to dispense with iteration, thus resulting in an efficient implicit scheme while retaining simplicity of implementation relative to contemporary block simultaneous methods. This is verified in a companion paper which presents results of computations carried out using the method.

HIGH RESOLUTION NVD DIFFERENCING SCHEME FOR ARBITRARILY UNSTRUCTURED MESHES

SUMMARY The issue of boundedness in the discretisation of the convection term of transport equations has been widely discussed. A large number of local adjustment practices has been proposed, including the well-known total variation diminishing (TVD) and normalised variable diagram (NVD) families of differencing schemes. All of these use some sort of an ‘unboundedness indicator’ in order to determine the parts of the domain where intervention in the discretisation practice is needed. These, however, all use the ‘far upwind’ value for each face under consideration, which is not appropriate for unstructured meshes. This paper proposes a modification of the NVD criterion that localises it and thus makes it applicable irrespective of the mesh structure, facilitating the implementation of ‘standard’ bounded differencing schemes on unstructured meshes. Based on this strategy, a new bounded version of central differencing constructed on the compact computational molecule is proposed and its performance is compared with other popular differencing schemes on several model problems. Copyright

A comparative study of subgrid scale models in homogeneous isotropic turbulence

Recently, a number of studies have indicated that Large Eddy Simulation (LES) models are fairly insensitive to the adopted Subgrid Scale (SGS) models. In order to study this and to gain further insight into LES, simulations of forced and decaying homogeneous isotropic turbulence have been performed for Taylor Re numbers between 35 and 248 using various SGS models, representative of the contemporary state of the art. The predictive capability of the LES concept is analyzed by comparison with DNS data and with results obtained from a theoretical model of the energy spectrum. The resolved flow is examined by visualizing the morphology and by analyzing the distribution of resolved enstrophy, rate of strain, stretching, SGS kinetic energy, and viscosity. Furthermore, the correlation between eigenvalues of the resolved rate of strain tensor and the vorticity is investigated. Although the gross features of the flow appear independent of the SGS model, pronounced differences between the models become apparent whe...

Application of a flame-wrinkling les combustion model to a turbulent mixing layer

The necessity for turbulent combustion modeling in the large-eddy simulation (LES) of premixed turbulent combustion is evident from the computational cost and the complexity of handling flame kinetics reaction mechanisms directly. In this paper, a new flame-wrinkling LES combustion model using conditional filtering is proposed. The model represents an alternative approach to the traditional flame-surface density based models in that the flame distribution is represented by a flame-wrinkle density function and that the effects of flame stretch and curvature are handled through a modeled transport equation for the perturbed laminar flame speed. For the purpose of validating the LES combustion model, LESs of isothermal and reacting shear layers formed at a rearward-facing step are carried out, and the results are compared with experimental data. For the isothermal case, the agreement between LES and the experimental data is excellent. For the reacting case, the evolution and topology of coherent structures is examined, and direct comparisons are made with time-averaged profiles of velocity and its fluctuations. temperature, and reaction products. Good agreement is obtained, to a large extent due to accurate modeling of the flame-wrinkle density but also to the novel treatment of the strain-rate effects on the laminar flame speed of the lean propane-air mixture.

Progress towards patient-specific computational flow modeling of the left heart via combination of magnetic resonance imaging with computational fluid dynamics.

A combined computational fluid dynamics (CFD) and magnetic resonance imaging (MRI) methodology has been developed to simulate blood flow in a subject-specific left heart. The research continues from earlier experience in modeling the human left ventricle using time-varying anatomical MR scans. Breathing artifacts are reduced by means of a MR navigator echo sequence with feedback to the subject, allowing a near constant breath-hold diaphragm position. An improved interactive segmentation technique for the long- and short-axis anatomical slices is used. The computational domain is extended to include the proximal left atrium and ascending aorta as well as the left ventricle, and the mitral and aortic valve orifices are approximately represented. The CFD results show remarkable correspondence with the MR velocity data acquired for comparison purposes, as well as with previously published in vivo experiments (velocity and pressure). Coherent vortex formation is observed below the mitral valve, with a larger anterior vortex dominating the late-diastolic phases. Some quantitative discrepancies exist between the CFD and MRI flow velocities, owing to the limitations of the MR dataset in the valve region, heart rate differences in the anatomical and velocity acquisitions, and to certain phenomena that were not simulated. The CFD results compare well with measured ranges in literature.© 2003 Biomedical Engineering Society.

Computational flow modeling of the left ventricle based on in vivo MRI data: initial experience.

AbstractA combined computational fluid dynamics (CFD) and magnetic resonance imaging (MRI) methodology has been developed to simulate blood flow in heart chambers, with specific application in the present study to the human left ventricle. The proposed framework employs MRI scans of a human heart to obtain geometric data, which are then used for the CFD simulations. These latter are accomplished by geometrical modeling of the ventricle using time-resolved anatomical slices of the ventricular geometry and imposition of inflow/outflow conditions at orifices notionally representing the mitral and aortic valves. The predicted flow structure evolution and physiologically relevant flow characteristics were examined and compared to existing information. The CFD model convincingly captures the three-dimensional contraction and expansion phases of endocardial motion in the left ventricle, allowing simulation of dominant flow features, such as the vortices and swirling structures. These results were qualitatively consistent with previous physiological and clinical experiments on in vivo ventricular chambers, but the accuracy of the simulated velocities was limited largely by the anatomical shortcomings in the valve region. The study also indicated areas in which the methodology requires improvement and extension.

CFD Analysis of a Low Friction Pocketed Pad Bearing

A CFD method has been applied to model lubricant flow behavior within linear pad bearings having large, closed pockets or recesses. The study shows that the presence of closed pockets can result in a significant reduction in bearing friction coefficient and that there are two different origins for this, depending on the bearing convergence ratio. At high convergence ratios, as used in conventional thrust hearings, a pocket located in the high-pressure region of the bearing produces a reduction in local shear stress and thus friction. This friction reduction is larger than the reduction in load support resulting from the presence of the pocket so there is a net overall reduction in friction coefficient. In low convergence ratio bearings, each pocket also acts as an effectively-independent step bearing and thereby generates a higher local pressure than would otherwise he the case. This results in the overall hearing having enhanced load support and thus a reduced friction coefficient. This effect is particularly large at very low convergence ratios when cavitation occurs in the pocket inlet.

Developments in CFD for industrial and environmental applications in wind engineering

An overview is provided of the capabilities and limitations of CFD as a tool for wind engineering, with particular reference to commercial CFD codes. The status of the modelling of turbulence, heat and mass transfer is briefly reviewed and developments in computer solution methodology are outlined, with emphasis on geometry-handling and mesh-generation capabilities and parallel computing. Examples are shown of recent applications in the built environment and other industries which illustrate the current state of art. The overall conclusion is that, although there are well-known weaknesses in the physics modelling, the level of prediction accuracy is already sufficient for some purposes.

Large Eddy Simulation of Primary Diesel Spray Atomization

One of the major problems in the CFD simulation of Diesel sprays is the incomplete and inadequate specification of initial conditions for the spray droplets. This is mainly a consequence of lack of understanding of the atomization process, which has inhibited the development of sufficiently general and accurate models for use in engine combustion simulations. In this paper a novel CFD approach, combining multiphase volume-of-fluid (VOF) and large eddy simulation (LES) methodologies, is used to perform quasi-direct transient fully three dimensional calculations of the atomization of a high-pressure diesel jet, providing detailed information on the processes and structures in the near nozzle region. The methodology allows separate examination of diverse influences on the breakup process and is expected in due course to provide a detailed picture of the mechanisms that govern the spray formation. It will therefore be a powerful tool for assisting in the development of accurate atomization models for practical applications. Our investigations so far have focused on the performance and initial validation of the methodology, in the absence of cavitation.

Measurements and large eddy simulations of turbulent premixed flame kernel growth

A combined experimental and large eddy simulation (LES) study of flame kernel growth in isotropic, homogenous turbulence has been carried out. LES calculations using the combustion methodology of Weller were compared with experimental measurements from a fan-stirred bomb for iso-octane and propane air mixtures at various turbulence intensities and pressures. For the purpose of model validation, the mean radius evolution was compared with experimental measurements, obtained from Schlieren photographs. Initially, a small laminar flame kernel was produced that burned at an increasing rate as it grew and was wrinkled by the turbulent flow field. It was also observed that at atmospheric pressure propaneair flames demonstrated less variability between experimental realizations than did iso-octane air flames High-variability combustion events were associated with the convection of the flame kernel away from the spark plug during ignition. Good agreement between experiments and calculations was obtaiend for the full range of conditions investigated in this study, and the LES results were able to reproduce some of the observed variability between experimental realizations as a result of turbulent interactions with the small kernel during ignition. These results provided further validation of the combustion model, though the simple ignitiion treatment did not reproduce the full range of ignition variability due to strain sensitivity.