Optimal control of viscous flow at high reynolds numbers

The most promising and most highly developed method for reducing drag in aerodynamics remains control of the flow by blowing and suction. In practice the main control problems remain the reduction of separation and the protracting of the transition of the boundary layer. These problems are solved mainly by experimental methods [1]. Meanwhile the main theoretical question remains unanswered: what is the theoretical minimum drag attainable by control through blowing (or suction)? In the present study an answer is given to this question for the cage of laminar flow round a body by a viscous incompressible fluid at high Reynolds numbers.     

Packet of gravity surface waves at high Reynolds numbers

Within the framework of the Lagrangian approach a method for describing a wave packet on the surface of an infinitely deep, viscous fluid is developed. The case, in which the inverse Reynolds number is of the order of the wave steepness squared is analyzed. The expressions for fluid particle trajectories are determined, accurate to the third power of the steepness. The conditions, under which the packet envelope evolution is described by the nonlinear Schrödinger equation with a dissipative term linear in the amplitude, are determined. The rule, in accordance with which the term of this type can be correctly added in the evolutionary equation of an arbitrary order is formulated.     

Anisotropic adaptive finite element method for magnetohydrodynamic flow at high Hartmann numbers

This paper presents an anisotropic adaptive finite element method (FEM) to solve the governing equations of steady magnetohydrodynamic (MHD) duct flow. A residual error estimator is presented for the standard FEM, and two-sided bounds on the error independent of the aspect ratio of meshes are provided. Based on the Zienkiewicz-Zhu estimates, a computable anisotropic error indicator and an implement anisotropic adaptive refinement for the MHD problem are derived at different values of the Hartmann number. The most distinguishing feature of the method is that the layer information from some directions is captured well such that the number of mesh vertices is dramatically reduced for a given level of accuracy. Thus, this approach is more suitable for approximating the layer problem at high Hartmann numbers. Numerical results show efficiency of the algorithm.     

Experimental study of flow past a square cylinder at high Reynolds numbers

 Measurements of two-components of velocity in the wake of a square cylinder using a hot-wire anemometer are reported. Two Reynolds numbers, namely 8700 and 17,625, have been considered. The measurements were carried out in a low-speed, low-turbulence wind tunnel. Benchmark experiments at much lower Reynolds numbers show good agreement between the present experiments and published results. At higher Reynolds numbers, the experimental data reveal anticipated trends in terms of wake recovery and turbulence decay. Both velocity and velocity fluctuations show symmetry about the wake axis. The experimental data have been compared with the large eddy simulation (LES) calculation reported by Wang et al. [University of Illinois at Urbana – Champaign (1996) Report CFD 96-03] and LDV measurements of Lyn et al. [J Fluid Mech (1995) 304: 285–319]. The agreement among the three sets is generally acceptable in terms of the time-averaged velocity components, but not the velocity fluctuations. The turbulence fluctuations in the present experiments are seen to be lower than in the referred work. The differences have been traced to factors such as the aspect ratio, blockage ratio and upstream turbulence. Experiments with increased upstream turbulence did show a reduction in the discrepancy between the present experiments and the published data. An assessment of the experimental data in terms of physical mechanisms revealed that (a) streamwise normal stresses were correlated with the vortex centers, and (b) the turbulence kinetic energy profiles are similar to the turbulence shear stress. Spectral analysis of the velocity signals was carried out in the present work. Energy transfer from the mean flow to the streamwise velocity fluctuation was confirmed in the near wake. A redistribution of the kinetic energy between the streamwise and transverse components of velocity over a longer distance downstream was subsequently observed. Received: 17 May 1999/Accepted: 29 December 1999     

Steady flow with separation past a thin airfoil at high Reynolds numbers

The results of calculating the steady separated flow of a viscous incompressible fluid past a 12% sinusoidal airfoil with and without a splitter plate are presented. The Navier—Stokes equations written in stream-function—vorticity variables are approximated in accordance with a central difference scheme and solved simultaneously by means of the direct method. The results obtained are analyzed from the standpoint of their consistency with the asymptotic theory based on the well-known three-deck scheme. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 155–160, March–April, 1994.     

Effect of free surface heat transfer on thermocapillary flow in double-layer fluid structures

In this paper, we examine the effect of heat transfer at the free encapsulant-air surface on thermocapillary flow in a rectangular melt-encapsulant double-layer fluid structure. We show that increased heat transfer to the double-layer system through the free surface weakens thermocapillary convection in the encapsulant phase and enhances the convection in the melt phase.     

DNS of passive scalar transport in turbulent channel flow at high Schmidt numbers

We perform DNS of passive scalar transport in low Reynolds number turbulent channel flow at Schmidt numbers up to Sc = 49. The high resolutions required to resolve the scalar concentration fields at such Schmidt numbers are achieved by a hierarchical algorithm in which only the scalar fields are solved on the grid dictated by the Batchelor scale. The velocity fields are solved on coarser grids and prolonged by a conservative interpolation to the fine-grid.

The trends observed so far at lower Schmidt numbers Sc  10 are confirmed, i.e. the mean scalar gradient steepens at the wall with increasing Schmidt number, the peaks of turbulent quantities increase and move towards the wall. The instantaneous scalar fields show a dramatic change. Observable structures get longer and thinner which is connected with the occurrence of steeper gradients, but the wall concentrations penetrate less deeply into the plateau in the core of the channel.

Our data shows that the thickness of the conductive sublayer, as defined by the intersection point of the linear with the logarithmic asymptote scales with Sc^−0.29. With this information it is possible to derive an expression for the dimensionless transfer coefficient K⁺ which is only dependent on Sc and Re_τ. This expression is in full accordance to previous results which demonstrates that the thickness of the conductive sublayer is the dominating quantity for the mean scalar profile.     

Free and confined jets at low Reynolds numbers

Free jets, and jets with tubular confinements, are investigated in the jet Reynolds number regime 80 Re_j 1000 being of interest for micro-jet pumps, among other applications. For issuing the jets, conventional (single-hole) nozzles as well as dual-hole nozzles of a particular design are used. Both flow visualization and LDA measurement indicate that, in agreement with previous findings, the jets issuing from conventional nozzles remain laminar up to large distances from the orifice. Thus there is but little entrainment of ambient fluid, and the performance of conventional nozzles in micro-jet pumps is rather poor. The dual-hole nozzles, on the other hand, are found to enforce transition to turbulent flow near the orifices. As a result, the entrainment rate is considerably increased, and the performance of jet pumps is improved when the dual-hole nozzles are applied. The experimental data are found to be in fair agreement with predictions based on mass and momentum balances.     

Peristaltic flow at finite Reynolds numbers

In this article the author discusses the results of a numerical investigtion of peristaltic flow at finite Reynolds numbers and finite wave numbers and amplitudes of the traveling wave at the channel walls. The limits of applicability of the data of the asymptotic analysis carried out [6] by means of separate expansions in powers of the Reynolds number and the wave number are determined. It is shown that with increase in the Reynolds number the possibility of transition, under certain conditions, to the flow structure corresponding to nonaxial trapping is preserved.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 11–15, May–June, 1985.The author wishes to thank E. M. Zhukhovitskii for his interest in the work.     

Numerical analysis of buoyant flow in a hemispherical enclosure at high Rayleigh numbers

A numerical analysis is presented for buoyancy driven flow of a Newtonian fluid contained in a two dimensional (R, ) hemispherical enclosure for high Rayleigh (Ra) numbers. It is assumed that the flow is driven by the uniformly distributed internal heat sources within the enclosure. All walls of the cavity are maintained at a constant temperature. Finite volume based SIMPLER algorithm has been used for the present analysis. Discretised governing equations, in primitive variables, are solved by a combination of Three Diagonal Matrix Algorithm (TDMA) and Point Successive Overrelaxation (PSOR) method. A benchmark solution prepared for a Ra number range of 10⁷ to 10¹² and Prandtl (Pr) number 7.0, shows an excellent agreement with the experimental results obtained from the open literature.     

An experimental investigation of viscoplastic flow past a circular cylinder at high Reynolds numbers

Summary The purpose of this work was to examine the high speed flow of viscoplastic fluid past a circular cylinder. Included in this work were measurements of the time-averaged wake length and the pressure and temperature distributions over the cylinder surface. The time-averaged wake length was very characteristic of viscoplasticity: The viscoplastic flow showed quite longer wake length than theNewtonian flow under certain conditions. It was found that there were the regions of stationary fluids adjacent to a cylinder and that they obstructed the heat transfer between the cylinder and fluid very much.

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Zusammenfassung Die vorliegende Arbeit befaßt sich mit der Untersuchung der Umströmung eines Kreiszylinders durch eine visko-plastische Flüssigkeit mit hoher Geschwindigkeit. Hierin eingeschlossen sind die Messung der mittleren Längenausdehnung des Totwasser-Gebiets sowie der Druck- und Temperaturverteilung über die Zylinderoberfläche. Die zeitlich gemittelte Längserstreckung des Totwasser-Gebiets stellt sich als eine für das visko-plastische Fließen charakteristische Größe heraus: Sie kommt erheblich größer heraus als fürnewtonsche Flüssigkeiten unter vergleichbaren Bedingungen. Man findet weiterhin am Zylinder anliegende stationäre Flüssigkeitsbereiche, welche die Wärmeübertragung zwischen Zylinder und Flüssigkeit sehr hemmen.

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With 16 figures and 1 table     

Annular liquid jets at high Reynolds numbers

The flow of annular liquid jets at high Reynolds numbers is analysed by means of the finite element method and the full‐Newton iteration scheme. Results have been obtained for various values of the inner to the outer diameter ratio and for non‐zero surface tension, using extremely long meshes. The annular film moves far from the symmetry axis at low values of the Reynolds number. At higher Reynolds numbers, the film moves towards the axis of symmetry and appears close to very far downstream, forming a round jet. Asymptotic results for the radius of the resulting round jet are provided. Copyright © 2003 John Wiley & Sons, Ltd.     

Asymptotic analysis of turbulent boundary layer flow on a flat plate at high Reynolds numbers

The equations of the turbulent boundary layer contain a small parameter — the reciprocal of the Reynolds number, which makes it possible to carry out an asymptotic analysis of the solutions with respect to that small parameter. Such analyses have been the subject of a number of studies [1–5]. In [2, 5] for closing the momentum equation algebraic Prandtl and turbulent viscosity models were used. In [1, 3, 4] the structure of the boundary layer was analyzed in general form without formulating specific closing hypothesis but under additional assumptions concerning the nature of the asymptotic behavior of the limiting solutions in the various regions.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 106–117, May-June, 1993.