Flow and bubble statistics of turbulent bubble-laden downflow channel

Direct numerical simulations of fully developed turbulent channel downflow at bulk Re equal to 6300, loaded with monodisperse bubbles at gas volume fractions α=0.5% , α=2.5% and α=10 have been carried out. Bubble deformability, surface tension, as well as discontinuity in the material properties across the bubble interfaces are explicitly accounted for. A full-scale channel of size 4πH × 2H × 4πH/3 in terms of the channel half-width H containing a number of bubbles up to O(103) is considered. The statistical structure of the bubbles, the probability density function describing the bubble velocity and the liquid kinetic energy spectra have been determined. A close range preferential clustering of the bubbles was found with a maximum density independent of the gas volume fraction at a separation distance of about 2.2R, with R the bubble radius. Preferential horizontal alignment and a general tendency to repulsion is shown for separation distances smaller than 3R. At larger separation distances a close to random distribution is observed for α=2.5% and α=10%, while tendency to vertical alignment is observed for α=0.5% . The pdf of the bubble velocity fluctuations was found to be well approximated by a Gaussian distribution. The liquid kinetic energy spectra in the channel core do not show a marked -3  scaling, which was previously reported for homogeneous isotropic turbulence and pseudo-turbulence

Leray and LANS-α\alpha modeling of turbulent mixing

Mathematical regularisation of the nonlinear terms in the Navier-Stokes equations provides a systematic approach to deriving subgrid closures for numerical simulations of turbulent flow. By construction, these subgrid closures imply existence and uniqueness of strong solutions to the corresponding modelled system of equations. We will consider the large eddy interpretation of two such mathematical regularisation principles, i.e., Leray and LANS$-\alpha$ regularisation. The Leray principle introduces a {\bfi smoothed transport velocity} as part of the regularised convective nonlinearity. The LANS$-\alpha$ principle extends the Leray formulation in a natural way in which a {\bfi filtered Kelvin circulation theorem}, incorporating the smoothed transport velocity, is explicitly satisfied. These regularisation principles give rise to implied subgrid closures which will be applied in large eddy simulation of turbulent mixing. Comparison with filtered direct numerical simulation data, and with predictions obtained from popular dynamic eddy-viscosity modelling, shows that these mathematical regularisation models are considerably more accurate, at a lower computational cost.Comment: 42 pages, 12 figure

Multigrid acceleration of a block structured compressible flow solver

We study a multiblock method for compressible turbulent flow simulations and present results obtained from calculations on a two-element airfoil. A cell-vertex or vertex-based spatial discretization method and explicit multistage Runge-Kutta time stepping are used. The vertex-based method is found to give better results than the cell-vertex method. In the latter method a larger amount of artificial dissipation is required since different control volumes are used for the discretization of the viscous and convective fluxes. The slow convergence of the time stepping method makes a multigrid acceleration technique indispensabl

Numerical calculation and experimental validation of safety valve flows at pressures up to 600 bar

A numerical valve model has been validated to predict the discharge capacity in accordance to the requirements of valve sizing method EN ISO 4126-1 and the opening characteristic of high-pressure safety valves. The valve is modeled with computational fluid dynamics software ANSYS CFX, and the model is extended with the Soave-Redlich–Kwong real-gas equation of state to allow calculations at pressures up to 3600 bar. A unique test facility has been constructed to perform valve function and capacity tests at operating pressures up to 600 bar with water and nitrogen. For gas flows, the numerical results and the experimental data on mass flow rates agree within 3%, whereas deviations in flow force are 12% on average. The inclusion of fluid-structure interaction in the numerical method improves the results for the flow force well and also gives insight into the valve dynamics of an opening safety valve. In a comparison between the experimentally and numerically determined liquid mass flow rates, a model extension accounting for cavitation reduces overpredictions by a factor of 2–20% for smaller disk lifts and decreases the deviations in flow force from 35 to 7%. At higher disk lifts, the effect of cavitation is less, and experimental and numerical mass flow rates agree within 4% and flow forces within 5%