Simulation of two-dimensional turbulence in a planar channel

A study is made of the two-dimensional flow of an incompressible viscous fluid in a planar channel at supercritical Reynolds number Re = 10⁴. Calculation of the flow over an appreciable time interval leads to the establishment of a statistically steady flow regime and stabilization of its averaged characteristics (the profile of the mean velocity, the mean pressure gradient, the pulsation energy, etc.). The calculations show that numerical simulation of turbulent flow of an incompressible fluid on the basis of the Navier-Stokes equations leads to qualitatively correct characteristics of this flow regime.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 26–35, November–December, 1982.We are very grateful to Yu. L. Levitan, B. D. Moiseenko, V. K. Sidorova, and I. N. Simakin, collaboration with whom helped us to do this work.     

Large-eddy simulation of transition to turbulence in a heated annular channel

One carries out three-dimensional large-eddy simulations of natural convection in a horizontal annulus using Smagorinsky's dynamic subgrid model. The onset of transition to turbulence and turbulent regimes are analyzed. The characteristics of unstable flows and their influence on the heat-transfer process are studied. To cite this article: E.L.M. Padilla, A. Silveira-Neto, C. R. Mecanique 333 (2005).     

Subharmonic transition to turbulence in channel flow

A direct numerical simulation of subharmonic transition to turbulence in channel flow has been performed. The stages of primary and secondary instability have been identified in the results leading to a staggered pattern of A-shaped vortices. The associated staggered symmetry has been found to persist up to rather late stages of the breakdown process. This symmetry rapidly disappears in the final stage of transition and a developed turbulent flow is attained. A pronounced difference in the development between the two channel halves is observed which is consistent with the predictions of secondary instability theory.     

Particle tracking method for measurements of turbulence properties in a curved channel

The turbulence properties of a curved channel flow have been measured by particle tracking method. The results reveal some characteristics of the structure for wall turbulence.     

Self-aeration and turbulence in a stepped channel: Influence of cavity surface roughness

The strong interactions between free-surface flows and atmospheric surroundings may lead to substantial air–water mixing with void fractions ranging from zero in clear-water to 100%. In this study, the air–water flow properties were studied in a large stepped water channel operating at large Reynolds numbers. Interactions between free-surface and cavity recirculation were systematically investigated in the skimming flow regime. Some surface roughness was introduced on the cavity walls and identical experiments were performed with several configurations. Basic results demonstrated some influence of step surface roughness on the flow properties leading to some counter-intuitive finding. The presence of cavity roughness was associated with higher flow velocities and comparatively lower turbulence levels. Distributions of bubble/droplet chords spanned over several orders of magnitude without significant influence of the cavity roughness. The distributions of turbulence levels and bubble count rates showed some correlation and highlighted strong interactions between entrained particles (bubbles, drops) and the flow turbulence.     

Turbulent transport dissimilarity with modulated turbulence structure in channel flow of viscoelastic fluid

This experimental study investigated the turbulent transport dissimilarity with a modulated turbulence structure in a channel flow of a viscoelastic fluid using simultaneous particle image velocimetry and planar laser-induced fluorescence measurements. An instantaneous dye concentration field with fluctuating velocity vectors showed that mass was transferred by hierarchically large-scale wavy motions with inclination. A co-spectral analysis showed that the spatial phase modulation of the streamwise velocity and dye concentration fluctuations for the wall-normal velocity fluctuation corresponded to the relaxation time. The occurrence of intense dye concentration fluctuation and small streamwise velocity fluctuation in a thin boundary layer caused dissimilar turbulent transport because of the non-zero negative correlation of the streamwise velocity and dye concentration fluctuations for the wall-normal velocity fluctuation only on large scales. This explains the turbulent transport dissimilarity which leads to the zero averaged Reynolds shear stress and non-zero wall-normal turbulent mass flux.     

Statistical characteristics of wall turbulence

The statistical turbulence characteristics obtained by direct numerical simulation of two flows, namely, flow in a circular pipe and flow in a channel with parallel walls, are given. The velocity profiles and the distributions of the statistical moments up to the fourth order inclusive are analyzed. The calculation results are compared with known experimental and numerical data.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 32–43, May–June, 1996.     

Effect of strong wall heating on turbulence statistics of a channel flow

Turbulence statistics of a channel flow with strong wall heating at Reynolds number of 14, 000 were investigated experimentally. The statistical quantities up to triple correlations were estimated, using data measured by a single component LDV. The wall temperature varies up to 1000 K. Rms values of streamwise and cross-stream velocities and their correlation decrease in the thermal boundary layer except near the wall. Near the wall, the ejection of low-speed fluid outward from the wall is intensified due to thermal expansion, and it cancels the decrease in statistical quantities. As a result, the statistical quantities do not vary apparently.Part of this work was supported by Tanikawa Fund, Promotion of Thermal Technology. The authors would like to thank to the referees for their valuable suggestion.     

Near-wall measurements of turbulence statistics in a fully developed channel flow with a novel laser Doppler velocity profile sensor

This paper reports on the measurements of the near-wall turbulence statistics in a fully developed channel flow. The flow measurements were carried out with a novel laser Doppler velocity profile sensor with a high spatial resolution. The sensor provides both the information of velocity and position of individual tracer particles inside the measurement volume. Hence, it yields the velocity profile inside the measurement volume, in principle, without the sensor being mechanically traversed. Two sensor systems were realized with different techniques. Typically the sensor has a relative accuracy of velocity measurement of 10⁻³ and the spatial resolution of a few micrometers inside the measurement volume of about 500 μm long. The streamwise velocity was measured with two independent sensor systems at three different Reynolds number conditions. The resulting turbulence statistics show a good agreement with available data of direct numerical simulations up to fourth order moment. This demonstrates the velocity profile sensor to be one of the promising techniques for turbulent flow research with the advantage of a spatial resolution more than one magnitude higher than a conventional laser Doppler technique.     

Distribution of turbulence energy dissipation rates in a Rushton turbine stirred mixer

An approximate method of measuring the turbulence energy dissipation rate () in mixers by use of laser-Doppler measurements of the velocity autocorrelation and turbulence energy was successful in yielding remarkably consistent values. The necessary corrections for periodic, non-dissipative velocity fluctuations were made by an autocorrelation method. Two modes of periodic fluctuation were found to be significant. Transformation of the corrected autocorrelations yielded completely normal turbulence energy spectra.List of symbols c fluctuating concentration, C–C - D impeller diameter - D molecular diffusivity - f() autocorrelation function - E ₁ (n) one-dimensional energy spectrum function - k turbulence energy (=q) - L _s macroscale of segregation - L _x integral velocity scale - N impeller rotation rate - N _Sc Schmidt number (v/D) - q turbulence energy (=k) - r radial distance from impeller shaft - R impeller radius - T tank diameter - U, V, W velocity in x, y, z directions - u, v, w velocity fluctuations - u _r , u , u _z fluctuating velocities in radial, tangential, and axial (shaft) directions - U _r , U , U _z velocities - z axial distance from impeller disk - Z tank height - turbulence energy dissipation rate - viscosity - time delay     

Investigation of turbulence structures in a drag-reduced turbulent channel flow with surfactant additive by stereoscopic particle image velocimetry

In the present study, we employed stereoscopic particle image velocimetry (PIV) to investigate the characteristics of turbulence structures in a drag-reduced turbulent channel flow with addition of surfactant. The tested drag-reducing fluid was a CTAC/NaSal/Water (CTAC: cetyltrimethyl ammonium chloride; NaSal: sodium salicylate) system at 25°C. The weight concentration of CTAC was 30 ppm. Stereoscopic PIV measurement was performed for a water flow (Re=1.1×10⁴) and a CTAC solution flow (Re=1.5×10⁴ with 54% drag reduction) in both the streamwise–spanwise and wall-normal-spanwise planes, respectively. The three-dimensionality of hairpin vortex structures in the near-wall region for wall-bounded turbulent flow was reproduced by conditionally averaging the stereoscopic two-dimensional-three-component velocity fields. A series of wall-normal vortex cores were found to align with the near-wall low-speed streaks with opposite vorticity signals at both sides of the streaks and with the vorticity decreased on average by about one order of magnitude in CTAC solution flow compared with water flow; the spanwise spacing between the near-wall low-speed streaks in the solution flow is increased by about 46%. The streamwise vorticity of the vortex cores appearing in the wall-normal-spanwise plane was also decreased by the use of drag-reducing surfactant additives.     

The concentration field in a turbulent channel flow with polymer injection at the wall

Instantaneous concentration profiles have been measured in turbulent water channel flows at 5 axial locations immediately downstream of a line, wall injection of a dyed 700 ppm polymer solution and for comparison, dyed water. Concentration was deduced from a line of fluoresced radiation that was stimulated by a laser beam directed through the dyed injectant and normal to the channel wall. Both statistical and time-resolved results show how the turbulent mixing is modified and damped when the injectant is a polymer solution. A version of this paper was presented at the 11th Symposium on Turbulence, University of Missouri-Rolla, Oct. 17–19, 1988     

Secondary instability and breakdown to turbulence in curved channel flow

The effect of curvature on laminar channel flow is studied experimentally, with a focus on secondary instability of the counter-rotating longitudinal vortices set up by the centrifugal force. It is shown that two types of secondary instability, with distinctly different frequencies, are at hand simultaneously, and their spatial distribution and growth are determined.     

Reconstruction of turbulence spectrum from transient characteristics of a shadow-instrument signal

With the investigation of turbulence using a shadow instrument with photoelectric recording, the statistical characteristics of the signal taken off from the instrument are used to obtain information on the statistics of the investigated medium [1, 2]. In situations where the investigated medium is moving perpendicular to the instrument axis (for example, with experiments in hydro- and aerodynamic tubes), it is convenient to use the transient characteristics of the signal. In the present article an investigation is made of the connection of the transient correlation function and the frequency spectrum of a shadow-instrument signal with the energy spectrum of the optical inhomogeneities in the medium; a method is given for reconstructing the spectrum of the inhomogeneities from the correlation function or the transient spectrum of the signal.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 73–77, January–February, 1978.     

Convection in a medium with spiral turbulence

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 22–26, November–December, 1990.     

Experimental investigation on turbulence modification in a horizontal channel flow at relatively low mass loading

Particle-laden flows in a horizontal channel were investigated by means of a two-phase particle image velocimetry (PIV) technique. Experiments were performed at a Reynolds number of 6 826 and the flow is seeded with polythene beads of two sizes, 60 μm and 110 μm. One was slightly smaller than and the other was larger than the Kolmogorov length scale. The particle loadings were relatively low, with mass loading ratio ranging from 5×10⁻⁴ to 4×10⁻² and volume fractions from 6×10⁻⁷ to 4.8×10⁻⁵, respectively. The results show that the presence of particles can dramatically modify the turbulence even under the lowest mass loading ratio of 5×10⁻⁴. The mean flow is attenuated and decreased with increasing particle size and mass loading. The turbulence intensities are enhanced in all the cases concerned. With the increase of the mass loading, the intensities vary in a complicated manner in the case of small particles, indicating complicated particle-turbulence interactions; whereas they increase monotonously in the case of large particles. The particle velocities and concentrations are also given. The particles lag behind the fluid in the center region but lead in the wall region, and this trend is more prominent for the large particles. The streamwise particle fluctuations are larger than the gas fluctuations for both sizes of particles, however their varying trend with the mass loadings is not so clear. The wall-normal fluctuations increase with increasing mass loadings. They are smaller in the 60 μm particle case but larger in the 110 μm particle case than those of the gas phase. It seems that the small particles follow the fluid motion to certain extent while the larger particles are more likely dominated by their own inertia. Finally, remarkable non-uniform distributions of particle concentration are observed, especially for the large particles. The inertia of particles is proved to be very important for the turbulence modification and particles behaviors and thus should be considered in horizontal channels. The project supported by the National Natural Science Foundation of China (50276021), and Program for New Century Excellent Talents in University, Ministry of Education (NCET-04-0708) The English text was polished by Yunming Chen.     

The spatial inhomogeneity of turbulence above a fully rough, packed bed in open channel flow

Single point turbulence statistics measured directly above and in close proximity to the wall in a fully developed, fully rough, turbulent open channel flow are reported. In order to investigate the spatial inhomogeneity of the turbulence, the measurements were obtained over a matrix of measurement points in a plane parallel to the roughness-bed surface. The measurements were obtained with a three-component laser Doppler velocimeter (3D-LDV) system. The turbulence statistics associated with the vertical velocity component, including conditioned mean vertical velocities, rms distributions, and mean vertical momentum fluxes are emphasized. For the Reynolds and Froude numbers associated with this investigation, and with the specific roughness geometry employed in this study (a packed bed of uniform-diameter spheres), it is found that the distribution of the local mean vertical velocity, <w>, has non-zero contributions over the roughness pattern and that this contributes to a mean net vertical momentum flux into the roughness bed. However, the net vertical momentum flux due to turbulent fluctuations is positive out of the bed, consistent with smooth-wall behavior. These results are relevant to the study of sediment entrainment and suspension/deposition as well as the exchange and transport of chemical species between the channel core flow and the fluid within the roughness bed. Received: 21 July 1998/Accepted: 20 November 1999