Application of a Fractional-Step Method to Incompressible Navier-Stokes Equations

Preface Part I. Turbulence: 1. Introduction 2. Coherent structures 3. Proper orthogonal decomposition 4. Galerkin projection Part II. Dynamical Systems: 5. Qualitative theory 6. Symmetry 7. One-dimensional 'turbulence' 8. Randomly perturbed systems Part III. 9. Low-dimensional Models: 10. Behaviour of the models Part IV. Other Applications and Related Work: 11. Some other fluid problems 12. Review: prospects for rigor Bibliography.

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Turbulence, Coherent Structures, Dynamical Systems and Symmetry

A spectral element method for fluid dynamics: Laminar flow in a channel expansion

Laser-Doppler measurements of velocity distribution and reattachment length are reported downstream of a single backward-facing step mounted in a two-dimensional channel. Results are presented for laminar, transitional and turbulent flow of air in a Reynolds-number range of 70 < Re < 8000. The experimental results show that the various flow regimes are characterized by typical variations of the separation length with Reynolds number. The reported laser-Doppler measurements do not only yield the expected primary zone of recirculating flow attached to the backward-facing step but also show additional regions of flow separation downstream of the step and on both sides of the channel test section. These additional separation regions have not been previously reported in the literature.Although the high aspect ratio of the test section (1:36) ensured that the oncoming flow was fully developed and two-dimensional, the experiments showed that the flow downstream of the step only remained two-dimensional at low and high Reynolds numbers.The present study also included numerical predictions of backward-facing step flow. The two-dimensional steady differential equations for conservation of mass and momentum were solved. Results are reported and are compared with experiments for those Reynolds numbers for which the flow maintained its two-dimensionality in the experiments. Under these circumstances, good agreement between experimental and numerical results is obtained.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112083002839

Experimental and Theoretical Investigation of Backward-Facing Step Flow

The dynamic subgrid-scale (SGS) model of Germano et al. (1991) is generalized for the large eddy simulation (LES) of compressible flows and transport of a scalar. The model was applied to the LES of decaying isotropic turbulence, and the results are in excellent agreement with experimental data and direct numerical simulations. The expression for the SGS turbulent Prandtl number was evaluated using direct numerical simulation (DNS) data in isotropic turbulence, homogeneous shear flow, and turbulent channel flow. The qualitative behavior of the model for turbulent Prandtl number and its dependence on molecular Prandtl number, direction of scalar gradient, and distance from the wall are in accordance with the total turbulent Prandtl number from the DNS data.

A dynamic subgrid‐scale model for compressible turbulence and scalar transport

A theoretical explanation for possible temperature discontinuities across a macroscopically-sharp plane solidification front

3D periodical turbulent flow induced by a low shear hyperboloid stirrer in a fully baffled stirred tank reactor is experimentally studied at a constant Reynolds number, 5600, by using a diode fiber laser-Doppler anemometer. The ratio D:T:H of the hyperboloid stirrer diameter, D = 50 mm, the inner tank diameter, T, and the filled fluid height, H, is 1:3:3. Three low stands of hyperboloid stirrer clearance, D/10, D/7 and D/5, are also targeted to evaluate influence on flow structure. The experimental results are applied to verification of CFD-code based on a standard k–e model.The flow field close to the hyperboloid stirrer is characterized by a series of vortex jets that are trailing periodically down within a radial extension of 0.5D to 0.7D. The maximum measured tangential velocity was 96% of the tip stirrer velocity. In this “near-of-flow area”, the kinetic energy is extensively dissipated itself due to impingement of velocity components. The axially-symmetric separation zone in the spatial form of λ-character induces two large-scale vortices above and below the separation. A highly rated kinetic energy lies within the head stream of λ-separation. Variation of the clearance at a factor less than D/5 sensibly influences flow structure and kinetic energy distribution. It is considered that computing on a turbulent hyperboloid flow field based on a k–e model at a relatively high Reynolds number may result in a discharge of kinetic energy induced within the “near-of area”.

Turbulent Flow Pattern of Hyperboloid Stirring Reactor

Computations of steady, ellipsoidal vortex rings with finite cores

Moire patterns to visually model laser-Doppler signals

In this paper, we describe detailed simulations of low mach number Newtonian flow through randomly generated porous media for a wide range of Reynolds numbers. The simulations were carried out using the lattice Boltzmann method, which has become an established tool for predicting flows in highly complex geometries. Several quantities were determined by an a posteriori analysis of the flow-fields: The pressure drop, the dissipation caused by shear and by elongation of the fluid, and the tortuosity. We were able to show that the pressure drop is mainly caused by the dissipation due to shear and elongation, and that the tortuosity is not related to the total dissipation, but to the relationship of dissipation and shear.

Franz Durst

Papers

A theoretical explanation for possible temperature discontinuities across a macroscopically-sharp plane solidification front

Turbulent Flow Pattern of Hyperboloid Stirring Reactor

Computations of steady, ellipsoidal vortex rings with finite cores

Moire patterns to visually model laser-Doppler signals

Numerical Analysis of the Pressure Drop in Porous Media Flow using the Lattice Boltzmann Computational Technique