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.

/pdf/turbulence-coherent-structures-dynamical-systems-and-fqofnixbu9.pdf

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

Slow motions of a solid spherical particle close to a viscous interface

A laser—Doppler sensor for flowrate measurements

Internal forced convection to mixtures of inert gases

In spite of the dramatic increase of the performance of recent supercomputers the direct numerical simulation (DNS) of turbulent flows is still an expensive venture in view of the high memory and CPU time requirements. Today, the DNS is limited to very low Reynolds number and simple flow geometries which are far away from technical relevance. Therefore, there is an increasing demand in the development of numerical schemes to simulate fluid flows resolving the turbulent scales in order to exploit existing and future supercomputers more efficiently. In that context, the lattice Boltzmann method have challenged the traditionally used DNS method based on FV or pseu-dospektral . The potential of these LBM have been clearly shown in various publications [4]. The goal of the present paper is to specify the advantages of the LBM to DNS more quantitatively and to make use of the LBM to investigate new phenomena related to wall bounded turbulence.

Franz Durst

Papers

Slow motions of a solid spherical particle close to a viscous interface

A laser—Doppler sensor for flowrate measurements

Internal forced convection to mixtures of inert gases

Direct Simulation with the Lattice Boltzmann Code BEST of Developed Turbulence in Channel Flows

Laser Techniques and Applications in Fluid Mechanics