scholarly journals The Influence of Hydrodynamic Changes in a System with a Pitched Blade Turbine on Mixing Power

Processes ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 68
Author(s):  
Jacek Stelmach ◽  
Czesław Kuncewicz ◽  
Szymon Szufa ◽  
Tomas Jirout ◽  
Frantisek Rieger
Keyword(s):  
Velocity Component ◽  
Tangential Velocity ◽  
Critical Value ◽  
Rotational Frequency ◽  
Water Levels ◽  
Liquid Stream ◽  
Piv Method ◽  
Pitched Blade Turbine ◽  
Turbine Impeller

This paper presents an analysis of hydrodynamics in a tank with a 45° and 60° pitched blade turbine impeller operating while emptying the mixer and with an axial agitator working during axial pumping-down of water at different water levels above the impeller. Measurements made with the PIV method confirmed the change in direction of pumping liquid after the level dropped below the critical value, with an almost unchanged liquid stream flowing through the mixer. It was found that an increase in the value of the tangential velocity in the area of the impeller took place and the quantity of this increase depended on the angle of the blade pitch and the rotational frequency of the impeller. Change in this velocity component increased the mixing power.

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 Transition Between Type I and Type III Bursts in Closed or Open Magnetic Field Lines

1980 ◽  
Vol 86 ◽  
pp. 363-368
Author(s):  
Monique G. Aubier
Keyword(s):  
Magnetic Field ◽  
Velocity Component ◽  
Low Frequency ◽  
Critical Value ◽  
Type I ◽  
Accelerated Electrons ◽  
Type Iii ◽  
Field Lines ◽  
Parallel Momentum ◽  
Open Magnetic Field

When studying the propagation of accelerated electrons outwards in the corona, we have shown that the perpendicular momentum of the electrons remaining after the type I process is transformed into parallel momentum during the propagation along the decreasing magnetic field, and that type III emission can occur when the parallel velocity component reaches a critical value. With this model we explain in particular the low frequency cut-off of type I emission, the characteristics of the type III bursts near their starting frequency and the transition between type III- and type I-like decameter emission observed in few cases.

Interception of two spheres with slip surfaces in linear Stokes flow

2007 ◽  
Vol 581 ◽  
pp. 129-156 ◽  
Author(s):  
H. LUO ◽  
C. POZRIKIDIS
Keyword(s):  
Integral Equations ◽  
Stokes Flow ◽  
Fourier Coefficients ◽  
Tangential Velocity ◽  
Critical Value ◽  
Element Distribution ◽  
Spherical Particles ◽  
Polar Coordinate System ◽  
Simple Shear Flow ◽  
Time Step

The interception of two spherical particles with arbitrary size in an infinite linear ambient Stokes flow is considered. The particle surfaces allow for slip according to the Navier–Maxwell–Basset law relating the shear stress to the tangential velocity. At any instant, the flow is computed in a frame of reference with origin at the centre of one particle using a cylindrical polar coordinate system whose axis of revolution passes through the centre of the second particle. Taking advantage of the axial symmetry of the boundaries of the flow in the particle coordinates, the problem is formulated as a system of integral equations for the zeroth, first, and second Fourier coefficients of the boundary traction with respect to the meridional angle. The force and torque exerted on each particle are determined by the zeroth and first Fourier coefficients, while the stresslet is determined by the zeroth, first, and second Fourier coefficients. The derived integral equations are solved with high accuracy using a boundary element method featuring adaptive element distribution and automatic time step adjustment according to the inter-particle gap. The results strongly suggest the existence of a critical value for the slip coefficient below which the surfaces of two particle collide after a finite interception time. The critical value depends on the relative initial particle positions. The particle stress tensor and coefficients of the linear and quadratic terms in the expansion of the effective viscosity of a dilute suspension in terms of the concentration in simple shear flow are discussed and evaluated. Surface slip significantly reduces the values of both coefficients and the longitudinal particle self-diffusivity.

Turbulence measurements with inclined hot-wires Part 2. Hot-wire response equations

1967 ◽  
Vol 28 (1) ◽  
pp. 177-182 ◽  
Author(s):  
F. H. Champagne ◽  
C. A. Sleicher
Keyword(s):  
Velocity Component ◽  
Wire Array ◽  
Tangential Velocity ◽  
Constant Current ◽  
Hot Wire ◽  
Tangential Velocity Component ◽  
Low Intensity ◽  
Hot Wires ◽  
Current Operation ◽  
Cosine Law

Hot-wire response equations to include the effects of the tangential velocity component as well as the non-linearities caused by high intensity turbulence are derived for linearized constant temperature operation. For low intensity turbulence similar equations are derived for constant current operation. The equations are applied to an X-wire array to determine the errors in selected turbulence quantities which arise from the assumption of cosine law cooling. The error depends upon the quantity measured, the method of operation, and [lscr ]/d. For [lscr ]/d = 200 the error ranges from 0 to 17%.

scholarly journals The Effect Of Tangential Velocity Component In Abrasive Jet Micro-Machining Of Borosilicate Glass

2021 ◽  
Author(s):  
Md. A. Hasem
Keyword(s):  
Borosilicate Glass ◽  
Velocity Component ◽  
Tangential Velocity ◽  
Micro Machining ◽  
Target Holder ◽  
Air Blast ◽  
Tangential Velocity Component ◽  
Erosion Testing ◽  
Oxide Particles ◽  
Velocity Effect

Generally two types of erosion testers are used in solid particle erosion testing: air blast erosion testers and mechanically powered erosion testers. In the first portion of this thesis, the feasibility of implementing a mechanically powered erosion tester for abrasive jet micro-machining applications using very small particles was studied. It was found that, due to the ultrahigh vacuum requirement, such a device would not be practical. Therefore, in the second part of the thesis, the designed rotary mechanism was utilized as a rotary disc target holder apparatus and blasted with a typical air blast system. The apparatus could add or deduct a tangential velocity component into the system, allowing for detailed studies of the effect that the tangential velocity component has on the erosion of borosilicate glass using 25-150 μm aluminum oxide particles. Although the tangential velocity effect has been ignored for brittle materials by most researchers, the present results show that it can have an important role in erosion rate.Generally two types of erosion testers are used in solid particle erosion testing: air blast erosion testers and mechanically powered erosion testers. In the first portion of this thesis, the feasibility of implementing a mechanically powered erosion tester for abrasive jet micro-machining applications using very small particles was studied. It was found that, due to the ultrahigh vacuum requirement, such a device would not be practical. Therefore, in the second part of the thesis, the designed rotary mechanism was utilized as a rotary disc target holder apparatus and blasted with a typical air blast system. The apparatus could add or deduct a tangential velocity component into the system, allowing for detailed studies of the effect that the tangential velocity component has on the erosion of borosilicate glass using 25-150 μm aluminum oxide particles. Although the tangential velocity effect has been ignored for brittle materials by most researchers, the present results show that it can have an important role in erosion rate.

scholarly journals Numerical Simulation of the Effects of the Helical Angle on the Decaying Swirl Flow of the Hole Cleaning Device

Processes ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 109 ◽  
Author(s):  
Jingyu Qu ◽  
Tie Yan ◽  
Xiaofeng Sun ◽  
Zijian Li ◽  
Wei Li
Keyword(s):  
Flow Direction ◽  
Tangential Velocity ◽  
Axial Flow ◽  
Critical Value ◽  
Swirl Flow ◽  
Swirl Number ◽  
Hole Cleaning ◽  
Helical Angle ◽  
Swirl Intensity ◽  
Cleaning Device

The application of the hole cleaning device in downhole is a new technology that can improve the problem of cuttings accumulation in the annulus and improve the hole cleaning effect of the wellbore during drilling. In this paper, the Reynolds Averaged Navier–Stokes model, together with the Realizable k-ε turbulence model, are used to perform transient simulations. The effects of rotational speed, blade shape, and helical angle on the initial swirl intensity and its decay behavior along the flow direction are studied. The swirl number, the initial swirl intensity, the decay rate, the tangential velocity distribution, and the variation of pressure are analyzed. The results indicate that the swirl number of the swirl flow exponentially decays along the flow direction. The straight blade and V-shaped blade have different swirl flow induction mechanisms. Under specific drilling parameters, the critical helical angle is determined for both types of blades. When the selection of the helical angle is close to the critical value, the swirl flow will be close to the axial flow, which is of little help in hole cleaning. Moreover, the rotation direction of swirl flow will change when the helical angle exceeds the critical value.

Dynamic Behavior of the Spherical Squeeze-Film Hybrid Bearing

1969 ◽  
Vol 91 (1) ◽  
pp. 149-160
Author(s):  
C. H. T. Pan ◽  
T. Chiang
Keyword(s):  
Radial Direction ◽  
Axial Direction ◽  
Critical Value ◽  
Rotational Frequency ◽  
Squeeze Film ◽  
Small Vibration ◽  
Hybrid Bearing ◽  
The Stability ◽  
Squeeze Number ◽  
Perturbation Solutions

The stability and vibration response of a spherical squeeze-film hybrid bearing were analyzed theoretically. Since the squeeze frequency is typically much higher than the vibration frequency, the asymptotic analysis for large squeeze number can be applied here. Perturbation solutions about the radially concentric position were obtained for small vibration amplitudes and small radial displacement. There is no limitation, however, in the values of vibration number (so long as it is small in comparison with the squeeze number), compressibility number, axial displacement ratio, and excursion ratio. Dynamic bearing reactions were computed based on the perturbation solutions. Results indicate that a spherical squeeze-film bearing is always stable in the axial direction. In the radial direction, however, instability about the radially concentric position is possible when there is journal rotation, the frequency of instability is exactly one half of the rotational frequency; the system would be stable if the mass is kept below the critical value. The analysis can be readily extended to compute the response to vibratory excitation in either the axial or the radial direction.

scholarly journals A study on measurement system of 3-D velocity component by PIV method

2001 ◽  
Vol 21 (2Supplement) ◽  
pp. 43-46
Author(s):  
Hirokazu KAMODA ◽  
Toshio SUZUKI ◽  
Yasuyuki TODA ◽  
Masahiro AZUMA ◽  
Tadayuki Fukui
Keyword(s):  
Measurement System ◽  
Velocity Component ◽  
Piv Method

scholarly journals R fluids

2008 ◽  
pp. 23-35 ◽  
Author(s):  
R. Caimmi
Keyword(s):  
Kinetic Energy ◽  
Velocity Component ◽  
Axial Velocity ◽  
Tangential Velocity ◽  
Random Motion ◽  
Moment Of Inertia ◽  
Random Velocity ◽  
Principal Axes ◽  
The Moment ◽  
Figure Rotation

A theory of collisionless fluids is developed in a unified picture, where nonrotating (?f1 = ?f2 = ?f3 = 0) figures with some given random velocity component distributions, and rotating (?f1 = ?f2 = ?f3 ) figures with a different random velocity component distributions, make adjoint configurations to the same system. R fluids are defined as ideal, self-gravitating fluids satisfying the virial theorem assumptions, in presence of systematic rotation around each of the principal axes of inertia. To this aim, mean and rms angular velocities and mean and rms tangential velocity components are expressed, by weighting on the moment of inertia and the mass, respectively. The figure rotation is defined as the mean angular velocity, weighted on the moment of inertia, with respect to a selected axis. The generalized tensor virial equations (Caimmi and Marmo 2005) are formulated for R fluids and further attention is devoted to axisymmetric configurations where, for selected coordinate axes, a variation in figure rotation has to be counterbalanced by a variation in anisotropy excess and vice versa. A microscopical analysis of systematic and random motions is performed under a few general hypotheses, by reversing the sign of tangential or axial velocity components of an assigned fraction of particles, leaving the distribution function and other parameters unchanged (Meza 2002). The application of the reversion process to tangential velocity components is found to imply the conversion of random motion rotation kinetic energy into systematic motion rotation kinetic energy. The application of the reversion process to axial velocity components is found to imply the conversion of random motion translation kinetic energy into systematic motion translation kinetic energy, and the loss related to a change of reference frame is expressed in terms of systematic motion (imaginary) rotation kinetic energy. A number of special situations are investigated in greater detail. It is found that an R fluid always admits an adjoint configuration where figure rotation occurs around only one principal axis of inertia (R3 fluid), which implies that all the results related to R3 fluids (Caimmi 2007) may be ex- tended to R fluids. Finally, a procedure is sketched for deriving the spin parameter distribution (including imaginary rotation) from a sample of observed or simulated large-scale collisionless fluids i.e. galaxies and galaxy clusters.

New Design Method for Spiral Casings Considering the Properties of the Impeller and Spiral Casing at Design and Off-Design Conditions and Numerical Verification With CFD

2018 ◽  
Author(s):  
Philipp Epple ◽  
Manuel Fritsche ◽  
Michael Steppert ◽  
Michael Steber
Keyword(s):  
Design Process ◽  
Flow Rate ◽  
Velocity Component ◽  
Tangential Velocity ◽  
Sectional Area ◽  
Cross Sectional ◽  
Flow Rates ◽  
Tangential Velocity Component ◽  
Design Point ◽  
Spiral Casing

Radial fans for industrial applications are very commonly operated with a spiral casing, also called volute. The function of the volute is to collect the air from the impellers outlet and to transport it to the fans outlet. In the volute the tangential velocity component of the impeller is transformed in a straight velocity component at the volute’s outlet. In the volute the static pressure is increased according to the cross sectional area of the volute. When the flow exits the impeller the flow rate is given basically by the radial velocity component times the outlet area of the impeller. In the volute, however, the flow rate is basically given by the tangential velocity component at the impeller exit and in the volute considering the conservation of angular momentum. Hence, there is only one operating point, i.e. the design point of the volute, where the flow rate in the impeller matches the flow rate in the volute. In the literature the design of the volute is performed at the design point only and the cross sectional area of the volute is usually computed distributing the flow rate linearly from the tongue to the exit of the volute. In this work an extended theoretical approach was developed considering the design point flow rate and off design flow rates. At the design point, the properties of the specific impeller, i.e. it’s radial and its tangential velocity components at the impeller’s exit are considered to design the volute. Furthermore, also the off-design characteristics of the impeller, i.e. its radial and tangential velocity components are considered in the design process of the volute. The flow rates in the impeller and in the volute match only at the design point, at off-design points the flow rates in the impeller and in the volute are different. This has an important impact on the design process of impeller – volute units. Each volute has also to be matched to the specific impeller. In the numerical part a usual volute was designed considering the properties of a particular impeller. The performance of the volute and of complete fan was investigated with the commercial Navier–Stokes Solver ANSYS CFX. A detailed analysis of the results and the flow conditions in volute as well as in the impeller-volute unit and a comparison with the results predicted by the new volute theory is given.

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