Liquid circulation in a cylindrical vessel with radial baffles and inclined blade impeller

1989 ◽  
Vol 54 (6) ◽  
pp. 1599-1611
Author(s):  
Ivan Fořt ◽  
Miloslav Hošťálek ◽  
Jaroslav Medek
Keyword(s):  
Stream Function ◽  
Stokes Equations ◽  
Laser Doppler Anemometry ◽  
Relative Size ◽  
Power Input ◽  
Cylindrical Vessel ◽  
Flat Bottom ◽  
Mean Velocity ◽  
Liquid Circulation ◽  
Radial Profiles

Liquid circulation was studied in a cylindrical vessel with radial baffles under the turbulent flow regime of liquid agitated gradually with the following types of four inclined blade impellers: impeller with plane blades inclined at the angle of 25°; impeller with asymmetrically profiled blades at the angle of 30°-17°; impeller with strength-profiled blades. By solving the turbulent (vortex) analogy of the Stokes equations for the creeping (non-inertial) laminar flow, the streamline distribution (the Stokes stream function) in the bulk of agitated charge was obtained for each of impellers studied (relative size d/D = 1/3, relative distance from the bottom H2/D = 1/3, relative vessel filling H/D = 1), placed axisymmetrically in the vessel and pumping the liquid towards its flat bottom. The zero values of the Stokes stream function at the bottom, walls, and charge liquid level, and further the radial profiles of axial and radial component of mean velocity in the cross sections under and above the impeller obtained experimentally by the laser-doppler anemometry on the assumption of axial symmetry of the agitated system studied were set as the boundary conditions for the solution of the partial differential equation considered. It follows from the results obtained that the homogenous circulation of agitated charge at the relatively lowest value of the impeller power input is reached when agitating with the asymmetrically profiled blade impeller which therefore can successfully replace the propeller mixer with airfoil profiled blades.

Description of the flow of mechanically agitated liquid in a system with cylindrical draft-tube and radial baffles

1987 ◽  
Vol 52 (6) ◽  
pp. 1416-1429 ◽  
Author(s):  
Ivan Fořt ◽  
Miloslav Hošťálek ◽  
Hans Dietrich Laufhütte ◽  
Alfons Bertram Mersmann
Keyword(s):  
Stream Function ◽  
High Speed ◽  
Draft Tube ◽  
Laser Doppler Anemometry ◽  
Vertex Angle ◽  
Flat Bottom ◽  
Mean Velocity ◽  
Radial Profiles ◽  
Flow Intensity ◽  
The Mean

A model is described of two-dimensional vortex turbulent flow of homogeneous liquid in a cylindrical tank with flat bottom and radial baffles at its walls agitated with an inclined plane blade impeller rotating in a cylindrical draft-tube. The obtained field of the mean Stokes stream function expresses the streamline distribution in the system. As the boundary conditions of the used solution of stream equation serve partly the values of the mean Stokes stream function on the system boundaries (bottom, liquid level, walls of tank and draft-tube, tank axis), partly the radial profiles of axial and radial components of mean velocity on the level of draft-tube lower base obtained by the laser-doppler anemometry. It follows from the comparison with results of previously published studies that in systems with cylindrical draft-tube and axial high-speed impeller, the convective flow intensity of agitated liquid is higher and the streamline distribution in system is more uniform providing that the conical bottom with 120° vertex angle is used instead of the flat bottom.

scholarly journals Study of Pumping Capacity of Pitched Blade Impellers

10.14311/380 ◽  
2002 ◽  
Vol 42 (4) ◽  
Author(s):  
I. Fořt ◽  
T. Jirout ◽  
R. Sperling ◽  
S. Jambere ◽  
F. Rieger
Keyword(s):  
Laser Doppler Anemometry ◽  
Radial Profile ◽  
Axial Flow ◽  
Power Input ◽  
Vessel Diameter ◽  
Energetic Efficiency ◽  
Turbulent Regime ◽  
Flat Bottom ◽  
Mean Velocity ◽  
Liquid Suspensions

A study was made of the pumping capacity of pitched blade impellers in a cylindrical pilot plant vessel with four standard radial baffles at the wall under a turbulent regime of flow. The pumping capacity was calculated from the radial profile of the axial flow, under the assumption of axial symmetry of the discharge flow. The mean velocity was measured using laser Doppler anemometry in a transparent vessel of diameter T = 400 mm, provided with a standard dished bottom. Three and six blade pitched blade impellers (the pitch angle varied within the interval a Îá24°; 45°ń) of impeller/vessel diameter ratio D/T = 0.36, as well as a three blade pitched blade impeller with folded blades of the same diameter, were tested. The calculated results were compared with the results of experiments mentioned in the literature, above all in cylindrical vessels with a flat bottom. Both arrangements of the agitated system were described by the impeller energetic efficiency, i.e, a criterion including in dimensionless form both the impeller energy consumption (impeller power input) and the impeller pumping effect (impeller pumping capacity). It follows from the results obtained with various geometrical configurations that the energetic efficiency of pitched blade impellers is significantly lower for configurations suitable for mixing solid-liquid suspensions (low impeller off bottom clearances) than for blending miscible liquids in mixing (higher impeller off bottom clearances).

Velocity Characteristics of Confined Coaxial Jets With and Without Swirl

1980 ◽  
Vol 102 (1) ◽  
pp. 47-53 ◽  
Author(s):  
M. A. Habib ◽  
J. H. Whitelaw
Keyword(s):  
Stokes Equations ◽  
Swirling Flow ◽  
Laser Doppler Anemometry ◽  
Velocity Ratio ◽  
Equation Model ◽  
Navier Stokes ◽  
Recirculation Region ◽  
Jet Flows ◽  
Mean Velocity ◽  
Navier Stokes Equations

Measured values of the velocity characteristics of turbulent, confined, coaxial-jet flows have been obtained, without swirl, for ratios of maximum annulus to pipe velocities of 1.0 and 3.0 and with a swirl number of 0.23 for a velocity ratio of 3.0. They were obtained by a combination of pressure probes, hot-wire and laser-Doppler anemometry. The results are compared with calculations, based on the solution of finite-difference forms of the steady, Navier-Stokes equations, and an effective-viscosity hypothesis. The measurements allow the influence of confinement and swirl to be quantified and show, for example, the increased tendency towards centerline recirculation which results from both. The results with the three types of instrumentation allow a comparison within the corner recirculation region which reveals that serious errors of interpretation of mean-velocity measurements need not arise. The two-equation model, although able to represent the non-swirling flow is less appropriate to the swirling flow and the reasons are indicated.

Hydrodynamic characteristics of flow in systems with turbine impellers

1983 ◽  
Vol 48 (2) ◽  
pp. 568-577 ◽  
Author(s):  
Ahmed Obeid ◽  
Ivan Fořt ◽  
Joël Bertrand
Keyword(s):  
Momentum Flux ◽  
Relative Size ◽  
Cylindrical Vessel ◽  
Hydrodynamic Characteristics ◽  
Model Parameters ◽  
Turbulent Regime ◽  
Mean Velocity ◽  
Proposed Model ◽  
Different Types ◽  
Basic Characteristics

The study deals with a phenomenological description of a flow leaving the blades of different types of turbine impellers, which are always placed in a cylindrical vessel with radial baffles under turbulent regime of liquid flow. The flow description is determined by three basic characteristics of the proposed model: i.e. the diameter of a cylindrical tangential jet a, the width parameter of a cylindrical tangential jet σ and the parameter of the intensity of momentum flux in the flow leaving the turbine A. All these parameters were calculated from the measured profiles of mean velocity for different types of turbines (standard, closed and with profiled blades) in systems of various dimensions. From the results follows that for geometrically similar agitated systems the model parameters have the same values; they vary with the type of turbine used and are independent on the relative size and position of the impeller in the system.

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.

Energy dissipation rate in a baffled vessel with pitched blade turbine impeller

1991 ◽  
Vol 56 (9) ◽  
pp. 1856-1867 ◽  
Author(s):  
Zdzisław Jaworski ◽  
Ivan Fořt
Keyword(s):  
Energy Dissipation ◽  
Cross Sections ◽  
Mechanical Energy ◽  
Vessel Diameter ◽  
Energy Dissipation Rate ◽  
Mean Velocity ◽  
Agitated Vessel ◽  
Radial Profiles ◽  
Pitched Blade Turbine ◽  
Turbine Impeller

Mechanical energy dissipation was investigated in a cylindrical, flat bottomed vessel with four radial baffles and the pitched blade turbine impeller of varied size. This study was based upon the experimental data on the hydrodynamics of the turbulent flow of water in an agitated vessel. They were gained by means of the three-holes Pitot tube technique for three impeller-to-vessel diameter ratio d/D = 1/3, 1/4 and 1/5. The experimental results obtained for two levels below and two levels above the impeller were used in the present study. Radial profiles of the mean velocity components, static and total pressures were presented for one of the levels. Local contribution to the axial transport of the agitated charge and energy was presented. Using the assumption of the axial symmetry of the flow field the volumetric flow rates were determined for the four horizontal cross-sections. Regions of positive and negative values of the total pressure of the liquid were indicated. Energy dissipation rates in various regions of the agitated vessel were estimated in the range from 0.2 to 6.0 of the average value for the whole vessel. Hydraulic impeller efficiency amounting to about 68% was obtained. The mechanical energy transferred by the impellers is dissipated in the following ways: 54% in the space below the impeller, 32% in the impeller region, 14% in the remaining part of the agitated liquid.

scholarly journals Urban Boundary Layers Over Dense and Tall Canopies

2021 ◽  
Author(s):  
Alexandros Makedonas ◽  
Matteo Carpentieri ◽  
Marco Placidi
Keyword(s):  
Packing Density ◽  
Laser Doppler Anemometry ◽  
Canopy Height ◽  
Roughness Sublayer ◽  
Average Height ◽  
Wind Tunnel Experiments ◽  
Mean Velocity ◽  
Flow Features ◽  
Stress Layer ◽  
Density Results

AbstractWind-tunnel experiments were carried out on four urban morphologies: two tall canopies with uniform height and two super-tall canopies with a large variation in element heights (where the maximum element height is more than double the average canopy height, $$h_{max}=2.5h_{avg}$$ h max = 2.5 h avg ). The average canopy height and packing density are fixed across the surfaces to $$h_{avg} = 80~\hbox {mm}$$ h avg = 80 mm , and $$\lambda _{p} = 0.44$$ λ p = 0.44 , respectively. A combination of laser Doppler anemometry and direct-drag measurements are used to calculate and scale the mean velocity profiles with the boundary-layer depth $$\delta $$ δ . In the uniform-height experiment, the high packing density results in a ‘skimming flow’ regime with very little flow penetration into the canopy. This leads to a surprisingly shallow roughness sublayer (depth $$\approx 1.15h_{avg}$$ ≈ 1.15 h avg ), and a well-defined inertial sublayer above it. In the heterogeneous-height canopies, despite the same packing density and average height, the flow features are significantly different. The height heterogeneity enhances mixing, thus encouraging deep flow penetration into the canopy. A deeper roughness sublayer is found to exist extending up to just above the tallest element height (corresponding to $$z/h_{avg} = 2.85$$ z / h avg = 2.85 ), which is found to be the dominant length scale controlling the flow behaviour. Results point toward the existence of a constant-stress layer for all surfaces considered herein despite the severity of the surface roughness ($$\delta /h_{avg} = 3 - 6.25$$ δ / h avg = 3 - 6.25 ). This contrasts with the previous literature.

Shape Optimization of Forward-Curved-Blade Centrifugal Fan with Navier-Stokes Analysis

2004 ◽  
Vol 126 (5) ◽  
pp. 735-742 ◽  
Author(s):  
Kwang-Yong Kim ◽  
Seoung-Jin Seo
Keyword(s):  
Response Surface ◽  
Stokes Equations ◽  
Computing Time ◽  
Relative Size ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Centrifugal Fan ◽  
Navier Stokes Equations ◽  
Design Variables ◽  
Curved Blade

In this paper, the response surface method using a three-dimensional Navier-Stokes analysis to optimize the shape of a forward-curved-blade centrifugal fan is described. For the numerical analysis, Reynolds-averaged Navier-Stokes equations with the standard k-ε turbulence model are discretized with finite volume approximations. The SIMPLEC algorithm is used as a velocity–pressure correction procedure. In order to reduce the huge computing time due to a large number of blades in forward-curved-blade centrifugal fan, the flow inside of the fan is regarded as steady flow by introducing the impeller force models. Four design variables, i.e., location of cutoff, radius of cutoff, expansion angle of scroll, and width of impeller, were selected to optimize the shapes of scroll and blades. Data points for response evaluations were selected by D-optimal design, and a linear programming method was used for the optimization on the response surface. As a main result of the optimization, the efficiency was successfully improved. Effects of the relative size of the inactive zone at the exit of impeller and momentum fluxes of the flow in scroll on efficiency were further discussed. It was found that the optimization process provides a reliable design of this kind of fan with reasonable computing time.

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.

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