Steady flow of a viscous incompressible fluid past two particles at moderate Reynolds numbers

A study is made of axisymmetric flow past two particles of spherical shape at Reynolds numbers 1 R 80. The flow patterns, pressure distributions, and values of the drag are investigated for different distances between the spheres. It is found that the drag depends nonmonotonically on the parameters that determine the flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 167–171, January–February, 1982.     

Magnetohydrodynamic flow past a drop at low Reynolds and Hartmann numbers

The flow of an electrically conductive liquid past a solid spherical particle at low Reynolds and Hartmann numbers in longitudinal and transverse magnetic fields was first investigated in [1,2]. The effect of a weak magnetic field on the strength of the resistance of a conductive drop in a dielectric medium was considered in [3]. In the present paper we consider the motion of a conductive liquid drop in an electrically conductive medium and calculate the strength of the resistance in the Stokes approximation for an arbitrary orientation of the uniform magnetic field and in the Oseen approximation for the case in which the direction of the magnetic field coincides with the direction of the oncoming stream. As in the previous studies, we do not consider the possibility of the formation of a double layer on the interface between the phases.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 19–25, November–December, 1978.The authors are grateful to G. I. Petrov and the participants in the seminar they conducted for their comments on the work.     

Measurements of turbulent flow in a channel at low Reynolds numbers

Normal and streamwise components of the velocity fields of turbulent flow in a channel at low Reynolds numbers have been measured with laser-Doppler techniques. The experiments duplicate the conditions used in current direct numerical simulations of channel flow, and good, but not exact, agreement is found for single-point moments through fourth order. In order to eliminate LDV velocity bias and to measure velocity spectra, the mean time interval between LDV signals was adjusted to be much smaller than the smallest turbulence time scale. Spectra of the streamwise and normal components of velocity at locations spanning the channel are presented.     

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.     

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     

Fluid oscillations in pipes at moderate Reynolds numbers

Little is known of the transition of the laminar motion of an oscillating fluid into turbulent motion and the resistance to motion in this region. The theoretical calculation of the critical value of the Reynolds number is very complex in this case and has not yet been successfully accomplished [1, 2]. Some experimental data on this subject are presented in [3]. Below are presented results of measurements of the critical values of the Reynolds number and the resistance forces for laminar and turbulent regimes of fluid oscillations in pipes.     

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     

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.     

Velocity measurements in a plane turbulent air jet at moderate Reynolds numbers

An experimental investigation of the moderate Reynolds number plane air jets was undertaken and the effect of the jet Reynolds number on the turbulent flow structure was determined. The Reynolds number, which was defined by the jet exit conditions, was varied between 1000 and 7000. Other initial conditions, such as the initial turbulence intensity, were kept constant throughout the experiments. Both hot-wire and laser Doppler anemometry were used for the velocity measurements. In the moderate Reynolds number regime, the turbulent flow structure is in transition. The average size and the number of the large scale of turbulence (per unit length of jet) was unaffected by the Reynolds number. A broadening of the turbulent spectra with increasing Reynolds number was observed. This indicated that there is a decrease in the strength of the large eddies resulting from a reduction of the relative energy available to them. This diminished the jet mixing with the ambient as the Reynolds number increased. Higher Reynolds numbers led to lower jet dilution and spread rates. On the other hand, at higher Reynolds numbers the dependence of jet mixing on Reynolds number became less significant as the turbulent flow structure developed into a self-preserving state.List of symbols b _u velocity half-width of the jet - C _u, C _u,0 constants defining the velocity decay rate - D nozzle width - E _u one dimensional power spectrum of velocity fluctuations - f frequency - K _u, K _u,0 constants defining the jet spread rate - k wavenumber (2f/U) - L longitudinal integral scale - R ₁₁ correlation function - r separation distance - Re jet Reynolds number (U ₀ D/v) - St Strouhal number (fD/U ₀) - t time - U axial component of the mean velocity - U _m mean velocity on the jet axis - U ₀ mean velocity at the jet exit - u the rms of u - u fluctuating component of the axial velocity - V lateral component of the mean velocity - fluctuating component of the lateral velocity - x axial distance from the nozzle exit - y lateral distance from the jet axis - z spanwise distance from the jet axis - v kinematic viscosity - time lag A version of this paper was presented as paper no. 86-0038 at the AIAA 24th Aerospace Sciences Meeting, Reno NV, USA, January 1986     

Turbulent flow in a channel at a low Reynolds number

A two-component laser Doppler velocimeter with high spatial and temporal resolution was used to obtain measurements for fully developed turbulent flow of water through a channel with an aspect ratio of 12 : 1 at Re=5700 (based on the centerline velocity and the half-height of the channel). Statistical quantities that were determined are the mean streamwise velocity, the root-mean-square of the fluctuations of the streamwise and the normal velocities, the Reynolds shear stress and higher order moments. Turbulence production is calculated from these quantities. Turbulence statistics obtained from experiments are compared with results from a direct numerical simulation at the same Reynolds number. The good agreement validates a recent DNS, at Re=5700, which is approximately twice as large as used in most previous studies. Received: 12 May 1997 / Accepted: 8 April 1998     

Influence of inlet shear on the 3-D flow past a square cylinder at moderate Reynolds number

Unsteady three-dimensional (3-D) numerical simulations of linear shear flow past a square cylinder at moderate Reynolds number (Re=200) are performed. The shear parameter (K) considered in this study is varied as 0.0, 0.1, and 0.2. For the uniform flow (K=0.0) case, the chosen Re falls in the transition Reynolds number range. The low frequency force pulsations of square cylinder transition phenomena are observed to decrease with increasing shear parameter. The evolution of streamwise vortical structures indicates a mode A spanwise instability in the uniform flow. Unlike in uniform flow, mixed mode A and mode B spanwise instability is observed in the case of a shear flow. The autocorrelation function of the lift and the drag coefficients is improved for any particular separation distance with increasing K.     

Flow of a viscous fluid past a flexible membrane at low Reynolds numbers

The numerical calculation of a steady two-dimensional viscous flow past a flexible membrane is treated. Both edges of the membrane are fixed in the flow and its chord is set normal to the flow. The Navier-Stokes equation in terms of the stream function and the vorticity is transformed to the body fitted coordinate system. The numerical calculations, based on a finite difference method and relaxation method, are carried out for several values of the membranes tension for cases when the Reynolds numbers are 5, 10 and 20. It is found that two different shapes of the membranes are possible at a given value of tension and Reynolds number: one with a small deformation, and the other with a large deformation. Two vortices appear in the concave region of the membrane if its deformation increases beyond a certain extent.     

Three-dimensionality of grooved channel flows at intermediate Reynolds numbers

 This paper describes the three-dimensional flow structure in grooved channels with different cavity lengths at intermediate Reynolds numbers. For steady flow, the three-dimensional effects are dominant near the side walls of the channel. However, after the onset of self-sustained oscillatory flow due to Tollmien–Schlichting waves as the primary instability, a secondary instability produces a three-dimensional flow with Taylor–Geortler-like vortical structure, at the bottom of the groove. This trend becomes more significant as the cavity length increases. Furthermore, the reason for three-dimensional flow is discussed using additional numerical analysis, and it is confirmed that the source of three-dimensional instability is the groove vortices due to the presence of side walls, rather than the channel traveling wave. Received: 7 September 1999/Accepted: 11 November 2000     

Rayleigh scattering temperature measurements in a plane turbulent air jet at moderate Reynolds numbers

Rayleigh scattering temperature measurements were made in a slightly heated plane jet at various Reynolds numbers and the effect of this parameter on the temperature field was determined. The axial and lateral distributions of the mean and rms temperature as well as the temperature spectra along the jet axis were determined. Results indicated that increasing Reynolds numbers led to lower levels of rms temperature and jet dilution in the moderate Reynolds number regime (between 700 and 2500). It was also found that slower spread rates of the thermal jet occured with larger Reynolds numbers in this regime.List of symbols b _T temperature half-width of the jet - C calibration constant for Rayleigh scattering optics - C _T, C _T,0 constants defining the temperature decay rate - D nozzle width - E _T power spectrum of temperature fluctuations - f frequency - I _L laser light intensity - I _R Rayleigh signal intensity - K _T, K _T,0 constants defining the jet spread rate - k wavenumber (2f/ U) - N total molecular number density - Re Reynolds number (U ₀D/) - T mean excess temperature - T _m mean excess temperature on the jet axis - T ₀ mean excess temperature at jet exit - T fluctuating temperature - U local mean velocity - U ₀ mean velocity at the jet exit - x axial distance from the nozzle exit - y lateral distance from the jet axis - z spanwise distance from the jet axis - Rayleigh scattering cross section - density - kinematic viscosity A version of this paper was presented as paper no 86-WA/ HT-98 at the 1986 ASME Winter Annual Meeting.     

The development of a plane laminar flow at low Reynolds numbers

Summary The development of a plane Poiseuille flow at low Reynolds numbers is studied; given any velocity distribution in the section x=0, it is possible to evaluate its evolution along the direction of motion, by means of quite simple calculation. A numerical example is also given.

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Sommario Si esamina l'evoluzione del profilo di velocità in moto piano laminare a bassi numeri di Reynolds. Assegnata una qualsiasi distribuzione di velocità nella sezione x=0, è possibile calcolare come questa si modifichi lungo il percorso. Si fornisce un esempio numerico.

     

Flow of a viscous fluid past a heterogeneous porous sphere at low Reynolds numbers

A flow past a heterogeneous porous sphere is investigated by using the perturbation theory. The flow through the sphere is divided into two zones, which are fully saturated with the viscous fluid, and the flow in these zones is governed by the Brinkman equation. The space outside the sphere, where a clear fluid flows, is also divided into two zones: the Navier–Stokes zone and the Oseen flow zone. The solutions on the interface inside the sphere are matched with the condition proposed by Merrikh and Mohammad. The stream function in the Navier–Stokes zone is matched with that on the sphere surface by the condition proposed by Ochoa-Tapia and Whitaker. It is found that the drag on the spherical shell decreases as the permeability toward the sphere boundary increases.     

Hypersonic flow past a plane magnetic dipole with parallel orientation of the magnetic moment and free-stream velocity vectors for moderate magnetic Reynolds numbers

The two-dimensional problem of hypersonic flow past a cylindrical body with a plane magnetic dipole in the presence of an external magnetic field is considered. The magnetic moment of the dipole is parallel to the free-stream velocity. The flow parameters correspond to a velocity of 7000 m/s at an altitude of approximately 65 km in the Earth’s atmosphere. The system of MHD equations (the Euler equations with volume MHD momentumand energy sources and the magnetic induction equation) was solved using the stabilization method. The calculations were carried out for two magnetic Reynolds numbers: (Re_m)₁ = 0.18 (corresponds to the parameters of the equilibrium ionized plasma in the shock layer) and (Re_m)₂ = 1.8 (the plasma conductivity increases by a factor of 10). The solutions obtained are analyzed, the effect of Re_m on the flow characteristics, namely, the shock wave stand-off from the body, the configuration of the vortex structures, and the aerodynamic and ponderomotive components of the body drag, is determined.