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

Mathematical tools are provided for computation of the scattered field produced by a spherical particle moving through the region of interference of two crossing laser beams. This formulation is readily applicable to laser Doppler and phase Doppler anemometers (PDAs). In particular, the geometry of PDAs is treated in the most general terms. The cases of very large and very small particles are considered in detail. In the first part the theory underlying the computer code STREU, which was produced during the present work, is discussed and relevant mathematical formulations are presented. Also, graphical tools are provided for the convenience of the designers.



In Part 2 the utility of the computer code is demonstrated with the help of examples in the area of phase Doppler anemometry. It is shown that the phase Doppler technique may be used for sizing of submicron particles in addition to large particles. Measurement of particle refractive index, in addition to the diameter, is also made possible.

Light Scattering Applied to LDA and PDA Measurements. Part 1: Theory and numerical treatments

Applications of Laser Anemometry to Fluid Mechanics

This paper deals with the derivations of the extended forms of the continuum conservation equations for ideal gas flows with heat and mass transfer, from upscaled molecular transport considerations. It is shown that for strong local temperature and/or density gradients, diffusive transport of momentum, heat, and mass over subcontinuum length scales gives rise to additional terms in the corresponding continuum level constitutive relationships. An exact analogy with kinematically hypothesized extended rheological forms is established by casting the expression for momentum flux in an equivalent linear form, with the postulation of a gradient-based hypothesis. Possible considerations of extending the theory to more general flow conditions are also discussed.

Derivations of extended Navier-Stokes equations from upscaled molecular transport considerations for compressible ideal gas flows: Towards extended constitutive forms

It is well known that dilute polymer solutions may exhibit strong viscoelastic flow effects when exposed to elongational flow fields with elongation rates that exceed certain “Onset”-conditions. Such flow fields occur in the converging-diverging flow passages of a porous matrix but also in regularly packed beds of spheres.

Franz Durst

Papers

Light Scattering Applied to LDA and PDA Measurements. Part 1: Theory and numerical treatments

Applications of Laser Anemometry to Fluid Mechanics

Derivations of extended Navier-Stokes equations from upscaled molecular transport considerations for compressible ideal gas flows: Towards extended constitutive forms

Viscoelastic flow of dilute polymer solutions in regularly packed beds

Comparison of measurements and numerical simulations of melt convection in Czochralski crystal growth of silicon