Introduction to heat transfer

High resolution schemes for hyperbolic conservation laws

A random flow generation (RFG) technique is presented, which can be used for initial/ inlet boundary generation in LES (Large-Eddy-Simulations) or particle tracking in LES/ RANS (Reynolds-Averaged Navier-Stokes) computations of turbulent flows. The technique is based on previous methods of synthesizing divergence-free vector fields from a sample of Fourier harmonics and allows to generate non-homogeneous anisotropic flow field representing turbulent velocity fluctuations. It was validated on the cases of boundary layer and flat plate flows. Applications of the technique to LES and particle tracking are considered

Random Flow Generation Technique for Large Eddy Simulations and Particle-Dynamics Modeling

A literature review on mechanisms and models for the coalescence process of fluid particles

A factor of safety method for quantitative estimates of grid-spacing and time-step uncertainties fbr solution verification is developed. It removes the two deficiencies of the grid convergence index and correction factor methods, namely, unreasonably small uncertainty when the estimated order of accuracy using the Richardson extrapolation method is greater than the theoretical order of accuracy and lack of statistical evidence that the interval of uncertainty at the 95% confidence level bounds the comparison error. Different error estimates are evaluated using the effectivity index. The uncertainty estimate builds on the correction factor method, but with significant improvements. The ratio of the estimated order of accuracy and theoretical order of accuracy P instead of the correction factor is used as the distance metric to the asymptotic range. The best error estimate is used to construct the uncertainty estimate. The assumption that the factor of safety is symmetric with respect to the asymptotic range was removed through the use of three instead of two factor of safety coefficients. The factor of safety method is validated using statistical analysis of 25 samples with different sizes based on 17 studies covering fluids, thermal, and structure disciplines. Only the factor of safety method, compared with the grid convergence index and correction factor methods, provides a reliability larger than 95% and a lower confidence limit greater than or equal to 1.2 at the 95% confidence level for the true mean of the parent population of the actual factor of safety. This conclusion is true for different studies, variables, ranges of P values, and single P values where multiple actual factors of safety are available. The number of samples is large and the range of P values is wide such that the factor of safety method is also valid for other applications including results not in the asymptotic range, which is typical in industrial and fluid engineering applications. An example for ship hydrodynamics is provided.

http://ftp.demec.ufpr.br/CFD/bibliografia/erros_numericos/Xing_Stern_2010.pdf

Factors of Safety for Richardson Extrapolation

Ship motions using single-phase level set with dynamic overset grids

Dynamic overset grids in OpenFOAM with application to KCS self-propulsion and maneuvering

Dynamic overset CFD simulations of wind turbine aerodynamics

: The single-phase level set method for unsteady viscous free surface flows is presented. In contrast to the standard level set method for incompressible flows, the single-phase level set method is concerned with the solution of the flow field in the water (or the denser) phase only. Some of the advantages of such an approach are that the interface remains sharp, the computation is performed within a fluid with uniform properties and that only minor computations are needed in the air. The location of the interface is determined using a signed distance function, and appropriate interpolations at the fluid/fluid interface are used to enforce the jump conditions. A reinitialization procedure has been developed for non-orthogonal grids with large aspect ratios. A convective extension is used to obtain the velocities at previous time-steps for the grid points in air, which allows a good estimation of the total derivatives. In this report we discuss the details of such implementations. The method was applied to three unsteady tests: a plane progressive wave, sloshing in a two-dimensional tank, and the wave diffraction problem in a surface ship, and the results compared against analytical solutions or experimental data. The method can in principle be applied to any problem in which the standard level-set method works, as long as the stress on the second phase can be specified (or neglected) and no bubbles appear in the flow during the computation.

Pablo M. Carrica

Papers

Ship motions using single-phase level set with dynamic overset grids

Dynamic overset grids in OpenFOAM with application to KCS self-propulsion and maneuvering

Dynamic overset CFD simulations of wind turbine aerodynamics

An unsteady single-phase level set method for viscous free surface flows

CFD verification and validation of added resistance and motions of KVLCC2 with fixed and free surge in short and long head waves