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 laser Doppler anemometer with a laser diode as the light source, has several advantages: i.e., low power consumption, compactness, and low cost. In order to be fully benefitted by these favorable characteristics, the measurement uncertainty, associated with wavefront distortion in the measuring volume, should be minimized. Furthermore, proper attention should be given to system misalignment caused by external perturbations, such as thermal expansion of the diode-collimator assembly. These considerations lead to a computational procedure for optimizing the layout of the semiconductor LDA system. Calculations are based on a generalized relation for fringe non-uniformity combined with a simulation model for the anemometry system. For this purpose, the optical field of a laser diode is described satisfactorily as a product of a Gaussian and a truncated Lorentzian distribution. The influence of various design parameters is examined by means of an extensive computational study as well as experimental evaluation involving precise scanning of the measuring volume. The performance is improved by employing a small focal length collimator and a large focal length front lens. For measurement of turbulence intensities smaller than 1%, it may become necessary to collect the signals in the side scatter and to use a frequency-domain signal processor. For such an application, temperature control may also be necessary, but it should be applied to the entire diode-collimator assembly and not just to the laser diode as suggested in previous publications.

Measurement accuracy of semiconductor LDA systems

https://www.lcpe.uni-sofia.bg/publications/1998/pdf/1998-10-KD.pdf

Stokes flow caused by the motion of a rigid sphere close to a viscous interface

Das viskoelastische Verhalten verdunnter makromolekularer Losungen wird anhand von Stromungen durch Zufallsschuttungen mit einheitlichem Kugeldurchmesser untersucht. Zur Beschreibung der experimentell beobachteten Polymereffekte wird das Konzept einer reprasentativen Deborahzahl angewandt, die sich fur die Porenstromung als Produkt aus der Relaxationszeit der Polymerflussigkeit und der effektiven Dehnrate im Porenraum ergibt. Zur Modellierung der polymeren Flussigkeit und zur Ableitung von Dehnviskositatsgleichungen werden Modellvorstellungen herangezogen, die auf der kinetischen Theorie verdunnter Hantelsuspensionen basieren. Fur endlich dehnbare, nichtlinear-elastische Hanteln als Modellmolekule erhalt man fur die Modellflussigkeit ein Zweiparametersystem (b, τH), welches unmittelbar in die viskoelastischen Kenngrosen einer reinen Dehnstromung eingeht. Die Porenstromung wird als eine solche Dehnstromung modelliert. Experimentelle Ergebnisse aus Porenstromungen zeigen, das der Einflus aller masgebenden stromungsmechanischen und physikalisch-chemischen Parameter, die das viskoelastische Verhalten von verdunnten Polymerlosungen bestimmen, von den theoretisch abgeleiteten Endbeziehungen korrekt beschrieben wird.

Die Charakterisierung viskoelastischer Fluide mit Hilfe ihrer Strömungseigenschaften in Kugelschüttungen

An extended phase-Doppler anemometry (PDA) system is described, which allows the user to measure the refractive index of spherical particles, in addition to their velocity, diameter and concentration. The extended PDA system incorporates two additional detectors on the receiving side. Each particle generates four Doppler signals. Phase shifts between two pairs of signals are recorded. The ratio between two measured values of phase shifts is a function of the particle refractive index. The phase ratio is shown to be fairly independent of particle velocity or diameter.



Calculations based on Mie scattering theory demonstrated the feasibility of the concept. Measurements with monosize droplets of glycerine-water mixture, covering the refractive index range 1.33–1.44, were used to verify the theoretical predictions. The instrument was also tested with spray flows.



It is also shown how the phase-Doppler technique may be used to distinguish between reflecting and refracting particles. This means that the extended phase-Doppler system may be employed to recognize particle material, and also to measure locally particle velocities, sizes and concentrations, in a multiphase flow with several transparent dispersed phases and one dispersed phase consisting of reflecting particles.

Franz Durst

Papers

Measurement accuracy of semiconductor LDA systems

Stokes flow caused by the motion of a rigid sphere close to a viscous interface

Die Charakterisierung viskoelastischer Fluide mit Hilfe ihrer Strömungseigenschaften in Kugelschüttungen

Extended Phase‐Doppler System for Characterization of Multiphase Flows

Experimental and Numerical Investigations of Plane Duct Flows With Sudden Contraction