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

Computation of fluid-structure interaction on lightweight structures

Experimental results on pressure losses of flows of dilute polymer solutions through porous media are summarized. The polymer products employed in this study consisted of partially hydrolyzed polyacrylamides (HPAM) with different degrees of hydrolysis. The effect of the hydrolysis on the pressure drop is investigated in a porous media test section designed to minimize polymer degradation. The investigations were carried out for various solvent conditions, and it is shown that the maximum increase in pressure drop is mainly dependent on the molecular weight of the polymers. The onset of the polymer action is measured for various fluid and solvent properties. Particular attention is given to measurements near θ-conditions. The results stress the importance of the solvent properties on the actions of the polymers and on the resultant pressure drop for porous media flows. The addition of salt ions to solutions of partially hydrolyzed polyacrylamides yields onset behavior previously observed for nonionic polymers. The differences measured between various solvent properties can be explained by the actual hydrodynamic molecule dimensions for a given molecular weight and polymer concentration. To quantify the influences of the solvent properties on the polymers, measurements were carried out in aqueous solutions for various pH values and therefore at various degrees of dissociation. The importance of separating polymer effects caused by their linear dimension in the solution from those that are introduced by and increase in solvent viscosity is shown. Measurements were performed to quantify the effects of solvent viscosity on the polymer action and to separate these effects from those due to changes in molecule dimensions. The implications of the present results are stressed in connection with applications of polymer solutions in tertiary oil recovery, and the positive features of the molecule actions on flow in such applications are described.

Flows of dilute hydrolyzed polyacrylamide solutions in porous media under various solvent conditions

Applications of hot-wire anemometers to velocity rneaaurements near walls can result in erroneous velocity data owing to additional heat losses to the wall. It is difficult to account for these errors if calibration data are used that were obtained in calibration test rigs without walls. This has been recognized in many studies in which hot-wires were applied to measurements in wall boundary-layer flows and different suggestions for corrections have been given. The present paper summarizes these suggested corrections and points out existing differences. It is also shown that some hot-wire measurements have been performed without any corrections being applied and reasons for this are given. Whereas most of the existing suggestions for wall corrections of hot-wire data are based on experiments, the present approach uses results of a numerical study.Assuming the problem to be two-dimensional and that the wire can be replaced by a line source of heat, a numerical study is carried out for the temperature distribution downstream of the wire, and computations are performed for the heat loss from the wire in presence of the wall. Computations are performed for two Merent boundary conditions representing ideally conducting and non-conducting materials. These different boundary conditions yield large differences in the computed heat losses from the wire, and these explain the existing differences in the experimentally obtained corrections. The numerical study also shows that the large heat losses for conducting walls are due to the distorted temperature distribution in the temperature wake of the wire.Some of the results of the numerical studies were experimentally verified by the authors and a procedure haa been developed to correct instantaneous hot-wire readings for additional heat losses to a wall. For non-conducting walls, the heat losses are much smaller and are negligible for most practical measurements.

Corrections of hot-wire anemometer measurements near walls

The present paper points out that the pressure drop of a porous media flow is only due to a small extent to the shear force term usually employed to derive the Kozeny—Darcy law. For a more correct derivation, additional shear terms have to be taken into account since the fluid is also exposed to elongational forces when it passes through the porous media matrix. These are usually not taken into account in the conventional theoretical treatment of flow through porous media as is explained in the literature. This explains why the available theoretical derivations of the Kozeny—Darcy relationship, which are based on one part of the shear-caused pressure drop only, require an adjustment of the constant in the theoretically derived equation to be applicable to experimental results. Details of this derivation are given in this paper and existing derivations are extended to yield better agreement with experiments. To verify experimentally some of the results of the theoretical derivation provided, porous media flows of dilute polymer solutions are studied experimentally. It is shown that the addition of small amounts of high molecular weight polymers to a solvent with Newtonian flow properties causes drastic pressure drop increases if the flow rate exceeds an onset flow rate corresponding to a critical Deborah number of the porous matrix-polymer solution system. This can only be explained if the flow field in the porous medium is exposed to shear and elongational strain. The extent of this interaction is deduced from experimental findings.

The nature of flows through porous media

This paper presents the results obtained during investigations carried out on a multifunctional stirrer test rig which was established at the Institute of Fluid Mechanics at the University of Erlangen-Nuremberg. The objective of the research work was to generate a reliable data basis for the validation of numerical simulations of the flow field in stirred-tank reactors. For the measurements advanced laser Doppler velocimetry including full refractive index matching and automated data acquisition was used. The flow field in this case was induced by a Rushton turbine which was constructed of transparent material in order to gain access to the important flow field within the turbine for the first time. The presentation of the large-scale flow field conforms the results presented in previous publications, but a higher resolution was realized. Mean flow and turbulence characteristics are presented. The turbulence length scale L was found to be about half the blade height, which is in good agreement with the length scales reported by other authors for Rushton turbines. The total access to the flow field permitted the mean flow and the turbulence kinetic energy distribution within the stirrer element to be determined in detail.

Franz Durst

Papers

Computation of fluid-structure interaction on lightweight structures

Flows of dilute hydrolyzed polyacrylamide solutions in porous media under various solvent conditions

Corrections of hot-wire anemometer measurements near walls

The nature of flows through porous media

Detailed LDV Measurements for Visualization of the Flow Field Within a Stirred-Tank Reactor Equipped with a Rushton Turbine