The flow of liquid in a stream from the standard turbine impeller

1979 ◽  
Vol 44 (3) ◽  
pp. 700-710 ◽  
Author(s):  
Ivan Fořt ◽  
Hans-Otto Möckel ◽  
Jan Drbohlav ◽  
Miroslav Hrach
Keyword(s):  
Reynolds Number ◽  
Kinematic Viscosity ◽  
Momentum Flux ◽  
Relative Size ◽  
Mean Velocity ◽  
Axial Profile ◽  
The Mean ◽  
Hot Film ◽  
Turbine Impeller

Profiles of the mean velocity have been analyzed in the stream streaking from the region of rotating standard six-blade disc turbine impeller. The profiles were obtained experimentally using a hot film thermoanemometer probe. The results of the analysis is the determination of the effect of relative size of the impeller and vessel and the kinematic viscosity of the charge on three parameters of the axial profile of the mean velocity in the examined stream. No significant change of the parameter of width of the examined stream and the momentum flux in the stream has been found in the range of parameters d/D ##m <0.25; 0.50> and the Reynolds number for mixing ReM ##m <2.90 . 101; 1 . 105>. However, a significant influence has been found of ReM (at negligible effect of d/D) on the size of the hypothetical source of motion - the radius of the tangential cylindrical jet - a. The proposed phenomenological model of the turbulent stream in region of turbine impeller has been found adequate for values of ReM exceeding 1.0 . 103.

Flow of liquid in a cylindrical vessel with a turbine impeller and radial baffles

1982 ◽  
Vol 47 (1) ◽  
pp. 226-239 ◽  
Author(s):  
Ivan Fořt ◽  
Ahmed Obeid ◽  
Vítězslav Březina
Keyword(s):  
Theoretical Model ◽  
Flow Pattern ◽  
Analytical Description ◽  
Cylindrical Vessel ◽  
Newtonian Liquid ◽  
Mean Velocity ◽  
Hot Film ◽  
System Geometry ◽  
Turbine Impeller

The study describes a theoretical model of flow pattern of a newtonian liquid in a flat-bottomed cylindrical vessel with radial baffles at wall agitated by a standard six-blade disc turbine impeller, under turbulent flow. The model, comprising the description of the field of main mean velocity components and of Stokes stream function in the system, is identified by experimental determination of velocity field by means of Pilot direction tubes and hot-film anemometer. The resulting analytical description of the flow pattern in the vessel corresponds well to that found experimentally. Knowing three parameters derived from the velocity profile of the stream streaking from the impeller, the description depends only on the system geometry.

Nonasymptotic behavior of developing turbulent pipe flow

1976 ◽  
Vol 54 (3) ◽  
pp. 268-278 ◽  
Author(s):  
J. K. Reichert ◽  
R. S. Azad
Keyword(s):  
Reynolds Number ◽  
Pipe Flow ◽  
Reynolds Numbers ◽  
Peak Position ◽  
Turbulent Pipe Flow ◽  
Shear Stresses ◽  
Mean Velocity ◽  
Inlet Region ◽  
The Mean ◽  
Hot Film

Detailed measurements of mean velocity U profiles, in the inlet 70 diameters of a pipe, show that the development of turbulent pipe flow is nonasymptotic. Experiments were done at seven Reynolds numbers in the range 56 000–15 3000. Contours of U and V fields are presented for two representative Reynolds numbers. A U component peak exceeding the fully developed values has been found to occur along the pipe centerline. The Reynolds number behavior of the peak position has been determined. Hot film measurements of the mean wall shear stresses in the inlet region also show a nonasymptotic development consistent with the mean velocity results.

scholarly journals Global energy fluxes in turbulent channels with flow control

2018 ◽  
Vol 857 ◽  
pp. 345-373 ◽  
Author(s):  
Davide Gatti ◽  
Andrea Cimarelli ◽  
Yosuke Hasegawa ◽  
Bettina Frohnapfel ◽  
Maurizio Quadrio
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Energy Dissipation ◽  
Velocity Field ◽  
Flow Control ◽  
Reynolds Shear Stress ◽  
Power Input ◽  
Energy Fluxes ◽  
Mean Velocity ◽  
The Mean

This paper addresses the integral energy fluxes in natural and controlled turbulent channel flows, where active skin-friction drag reduction techniques allow a more efficient use of the available power. We study whether the increased efficiency shows any general trend in how energy is dissipated by the mean velocity field (mean dissipation) and by the fluctuating velocity field (turbulent dissipation). Direct numerical simulations (DNS) of different control strategies are performed at constant power input (CPI), so that at statistical equilibrium, each flow (either uncontrolled or controlled by different means) has the same power input, hence the same global energy flux and, by definition, the same total energy dissipation rate. The simulations reveal that changes in mean and turbulent energy dissipation rates can be of either sign in a successfully controlled flow. A quantitative description of these changes is made possible by a new decomposition of the total dissipation, stemming from an extended Reynolds decomposition, where the mean velocity is split into a laminar component and a deviation from it. Thanks to the analytical expressions of the laminar quantities, exact relationships are derived that link the achieved flow rate increase and all energy fluxes in the flow system with two wall-normal integrals of the Reynolds shear stress and the Reynolds number. The dependence of the energy fluxes on the Reynolds number is elucidated with a simple model in which the control-dependent changes of the Reynolds shear stress are accounted for via a modification of the mean velocity profile. The physical meaning of the energy fluxes stemming from the new decomposition unveils their inter-relations and connection to flow control, so that a clear target for flow control can be identified.

Prediction of the Maximum Number of Repetitions and Repetitions in Reserve From Barbell Velocity

2018 ◽  
Vol 13 (3) ◽  
pp. 353-359 ◽  
Author(s):  
Amador García-Ramos ◽  
Alejandro Torrejón ◽  
Belén Feriche ◽  
Antonio J. Morales-Artacho ◽  
Alejandro Pérez-Castilla ◽  
...  
Keyword(s):  
Body Mass ◽  
General Equation ◽  
Bench Press ◽  
Body Height ◽  
Strong Relationship ◽  
Training Set ◽  
Mean Velocity ◽  
The Mean ◽  
Acceptable Reliability

Purpose: To provide 2 general equations to estimate the maximum possible number of repetitions (XRM) from the mean velocity (MV) of the barbell and the MV associated with a given number of repetitions in reserve, as well as to determine the between-sessions reliability of the MV associated with each XRM. Methods: After determination of the bench-press 1-repetition maximum (1RM; 1.15 ± 0.21 kg/kg body mass), 21 men (age 23.0 ± 2.7 y, body mass 72.7 ± 8.3 kg, body height 1.77 ± 0.07 m) completed 4 sets of as many repetitions as possible against relative loads of 60%1RM, 70%1RM, 80%1RM, and 90%1RM over 2 separate sessions. The different loads were tested in a randomized order with 10 min of rest between them. All repetitions were performed at the maximum intended velocity. Results: Both the general equation to predict the XRM from the fastest MV of the set (CV = 15.8–18.5%) and the general equation to predict MV associated with a given number of repetitions in reserve (CV = 14.6–28.8%) failed to provide data with acceptable between-subjects variability. However, a strong relationship (median r2 = .984) and acceptable reliability (CV < 10% and ICC > .85) were observed between the fastest MV of the set and the XRM when considering individual data. Conclusions: These results indicate that generalized group equations are not acceptable methods for estimating the XRM–MV relationship or the number of repetitions in reserve. When attempting to estimate the XRM–MV relationship, one must use individualized relationships to objectively estimate the exact number of repetitions that can be performed in a training set.

scholarly journals Model-based scaling of the streamwise energy density in high-Reynolds-number turbulent channels

2013 ◽  
Vol 734 ◽  
pp. 275-316 ◽  
Author(s):  
Rashad Moarref ◽  
Ati S. Sharma ◽  
Joel A. Tropp ◽  
Beverley J. McKeon
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Low Rank ◽  
Navier Stokes ◽  
Mean Velocity ◽  
Navier Stokes Equations ◽  
Self Similar ◽  
The Mean ◽  
High Reynolds

AbstractWe study the Reynolds-number scaling and the geometric self-similarity of a gain-based, low-rank approximation to turbulent channel flows, determined by the resolvent formulation of McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382), in order to obtain a description of the streamwise turbulence intensity from direct consideration of the Navier–Stokes equations. Under this formulation, the velocity field is decomposed into propagating waves (with single streamwise and spanwise wavelengths and wave speed) whose wall-normal shapes are determined from the principal singular function of the corresponding resolvent operator. Using the accepted scalings of the mean velocity in wall-bounded turbulent flows, we establish that the resolvent operator admits three classes of wave parameters that induce universal behaviour with Reynolds number in the low-rank model, and which are consistent with scalings proposed throughout the wall turbulence literature. In addition, it is shown that a necessary condition for geometrically self-similar resolvent modes is the presence of a logarithmic turbulent mean velocity. Under the practical assumption that the mean velocity consists of a logarithmic region, we identify the scalings that constitute hierarchies of self-similar modes that are parameterized by the critical wall-normal location where the speed of the mode equals the local turbulent mean velocity. For the rank-1 model subject to broadband forcing, the integrated streamwise energy density takes a universal form which is consistent with the dominant near-wall turbulent motions. When the shape of the forcing is optimized to enforce matching with results from direct numerical simulations at low turbulent Reynolds numbers, further similarity appears. Representation of these weight functions using similarity laws enables prediction of the Reynolds number and wall-normal variations of the streamwise energy intensity at high Reynolds numbers (${Re}_{\tau } \approx 1{0}^{3} {\unicode{x2013}} 1{0}^{10} $). Results from this low-rank model of the Navier–Stokes equations compare favourably with experimental results in the literature.

Measurements of the Velocity Field Downstream of an Impeller

1996 ◽  
Vol 118 (3) ◽  
pp. 602-610 ◽  
Author(s):  
Per Petersson ◽  
Magnus Larson ◽  
Lennart Jo¨nsson
Keyword(s):  
Velocity Field ◽  
Momentum Flux ◽  
Laser Doppler Velocimeter ◽  
Self Similarity ◽  
Mean Velocity ◽  
Measured Velocity ◽  
Swirling Jets ◽  
Axial Velocity Profile ◽  
Two Component ◽  
The Mean

The velocity field downstream of a model impeller operating in water was measured using a two-component laser doppler velocimeter. The investigation focussed on the spatial development of the mean velocity in the axial, radial, and circumferential direction, although simultaneous measurements were performed of the velocity unsteadiness from which turbulence characteristics were inferred. The measurements extended up to 12 impeller diameters downstream of the blades displaying the properties of the generated swirling jet both in the zone of flow establishment and the zone of established flow. The division between these zones was made based on similarity of the mean axial velocity profile. Integral properties of the flow such as volume and momentum flux were computed from the measured velocity profiles. The transverse spreading of the impeller jet and its development towards self-similarity were examined and compared with non-swirling jets and swirling jets generated by other means.

Effect of Upstream Flow Processes on Hydrodynamic Development in a Duct

1977 ◽  
Vol 99 (3) ◽  
pp. 556-560 ◽  
Author(s):  
E. M. Sparrow ◽  
C. E. Anderson
Keyword(s):  
Reynolds Number ◽  
Reynolds Numbers ◽  
Center Line ◽  
Viscous Effects ◽  
Mean Velocity ◽  
Inertia Effects ◽  
Reynolds Number Flow ◽  
Compact Size ◽  
Number Flow ◽  
The Mean

Consideration is given to the developing laminar flow in a parallel plate channel, with the fluid being drawn from a large upstream space. The flow fields upstream and downstream of the channel inlet were solved simultaneously. A finite-difference technique was employed which was facilitated by a coordinate transformation that telescoped the broadly extended flow domain into a more compact size. For the solutions, the Reynolds number was assigned values from 1 to 1000, covering the range from viscous-dominated flows to those where both viscous and inertia effects are relevant. Streamline maps indicate that whereas a low Reynolds number flow glides smoothly into the channel, a high Reynolds number flow has to turn sharply to enter the channel, with the result that the sharply turning fluid tends to overshoot at first and then readjust. A significant amount of upstream predevelopment occurs at low and intermediate Reynolds numbers. Thus, for example, at Re = 1 and 100, the center-line velocities at inlet are, respectively, 1.37 and 1.13 times the mean velocity (the fully developed center-line velocity is 1.5 times the mean). The upstream pressure drop, measured in terms of the velocity head, is substantially increased by viscous effects at low and intermediate Reynolds numbers.

An experimental investigation of pulsating turbulent water flow in a tube

1971 ◽  
Vol 46 (1) ◽  
pp. 43-64 ◽  
Author(s):  
J. H. Gerrard
Keyword(s):  
Reynolds Number ◽  
Velocity Profile ◽  
Water Flow ◽  
Cylindrical Tube ◽  
Flow Speed ◽  
Mean Flow ◽  
Mean Velocity ◽  
Central Plateau ◽  
Transition Range ◽  
The Mean

Experiments were made on a pulsating water flow at a mean flow Reynolds number of 3770 in a cylindrical tube of diameter 3·81 cm. Pulsations were produced by a piston oscillating in simple harmonic motion with a period of 12 s. Turbulence was made visible by means of a sheet of dye produced by electrolysis from a fine wire stretched across a diameter. The sheet of dye is contorted by the turbulent eddies, and ciné-photography was used to find the velocity of convection which was shown to be the flow speed except in certain circumstances which are discussed. By subtracting the mean flow velocity profile the profile of the component of the motion oscillating at the imposed frequency was determined.The Reynolds number of these experiments lies in the turbulent transition range, so that large effects of laminarization are observed. In the turbulent phase, the velocity profile was found to possess a central plateau as does the laminar oscillating profile. The level and radial extent of this were little different from the laminar ones. Near to the wall, the turbulent oscillating profile is well represented by the mean velocity power law relationship, u/U ∝ (y/a)1/n. In the laminarized phase, the turbulent intensity is considerably reduced at this Reynolds number. The velocity profile for the whole flow (mean plus oscillating) relaxes towards the laminar profile. Laminarization contributes appreciably to the oscillating component.Extrapolation of the results to higher Reynolds numbers and different frequencies of oscillation is suggested.

Experimental Investigation of a High Velocity Gaseous Jet Injection Into an Oscillating Crossflow

2021 ◽  
Author(s):  
Jinkwan Song ◽  
Johnathan Wilson ◽  
Jong Guen Lee
Keyword(s):  
Velocity Fluctuation ◽  
Momentum Flux ◽  
Modulation Frequency ◽  
Concentration Field ◽  
Flux Ratio ◽  
Mean Velocity ◽  
Potential Core ◽  
Crossflow Velocity ◽  
The Mean ◽  
Jet Penetration

Abstract This paper presents the experimental results of a gaseous jet injected into an oscillating-air crossflow. The jet to crossflow momentum flux ratios are chosen as 19, 30 and 58, and the mean air crossflow velocities are chosen as 10m/s, 25 m/s, and 60 m/s. The crossflow is modulated at frequencies up to 280 Hz with a maximum crossflow velocity fluctuation of 30% of its mean velocity. Acetone planar laser-induced fluorescence is used to record the instantaneous jet concentration field. Three distinct regions are observed near the injection location (x/d &lt; 18); the jet core, the fast bending zone, and the fully developed plume zone. The location of the end of potential core can be determined primarily by the momentum flux ratio. Based on observations of these three regions, a set of correlations for the trajectory of maximum jet concentration is proposed for the potential core region and for the fully developed plume zone. The potential core responds quasi-steadily to the crossflow oscillation and the fluctuation of penetration of the potential core zone linearly increases with respect to the crossflow velocity fluctuation level. The jet penetration under oscillating crossflow is slightly lower than that under steady crossflow, especially when the mean crossflow velocity is low (10–25 m/s). However, the differences of trajectories between the oscillating and the steady crossflow cases become almost negligible as the mean crossflow velocity increases further. The axial decay of jet concentration under oscillating crossflow occurs at faster rate than that under steady crossflow, indicating that the oscillating air crossflow enhances the mixing between the jet and the crossflow. The vertical jet concentration profile at different axial location confirms that the main effect of crossflow modulation is enhanced mixing of jet with crossflow. However, no noticeable effect of modulation frequency of crossflow on the jet penetration is found.

scholarly journals Nonlinear waves with a threefold rotational symmetry in pipe flow: influence of a strongly shear-thinning rheology

2017 ◽  
Vol 818 ◽  
pp. 595-622
Author(s):  
Emmanuel Plaut ◽  
Nicolas Roland ◽  
Chérif Nouar
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Nonlinear Waves ◽  
Pipe Flow ◽  
Rotational Symmetry ◽  
Shear Thinning ◽  
Transition To Turbulence ◽  
Mean Velocity ◽  
The Mean ◽  
The One

In order to model the transition to turbulence in pipe flow of non-Newtonian fluids, the influence of a strongly shear-thinning rheology on the travelling waves with a threefold rotational symmetry of Faisst & Eckhardt (Phys. Rev. Lett., vol. 91, 2003, 224502) and Wedin & Kerswell (J. Fluid Mech., vol. 508, 2004, pp. 333–371) is analysed. The rheological model is Carreau’s law. Besides the shear-thinning index $n_{C}$, the dimensionless characteristic time $\unicode[STIX]{x1D706}$ of the fluid is considered as the main non-Newtonian control parameter. If $\unicode[STIX]{x1D706}=0$, the fluid is Newtonian. In the relevant limit $\unicode[STIX]{x1D706}\rightarrow +\infty$, the fluid approaches a power-law behaviour. The laminar base flows are first characterized. To compute the nonlinear waves, a Petrov–Galerkin code is used, with continuation methods, starting from the Newtonian case. The axial wavenumber is optimized and the critical waves appearing at minimal values of the Reynolds number $\mathit{Re}_{w}$ based on the mean velocity and wall viscosity are characterized. As $\unicode[STIX]{x1D706}$ increases, these correspond to a constant value of the Reynolds number based on the mean velocity and viscosity. This viscosity, close to the one of the laminar flow, can be estimated analytically. Therefore the experimentally relevant critical Reynolds number $\mathit{Re}_{wc}$ can also be estimated analytically. This Reynolds number may be viewed as a lower estimate of the Reynolds number for the transition to developed turbulence. This demonstrates a quantified stabilizing effect of the shear-thinning rheology. Finally, the increase of the pressure gradient in waves, as compared to the one in the laminar flow with the same mass flux, is calculated, and a kind of ‘drag reduction effect’ is found.

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