Simple explicit model of liquid mean flow in region above axial impeller

1985 ◽  
Vol 50 (11) ◽  
pp. 2396-2410
Author(s):  
Miloslav Hošťálek ◽  
Ivan Fořt
Keyword(s):  
Vortex Flow ◽  
Flow Model ◽  
Quantitative Agreement ◽  
Mean Flow ◽  
Flat Bottom ◽  
Proposed Model ◽  
Minimum Number ◽  
The Mean ◽  
Model Equations ◽  
Radial Circulation

The study describes a method of modelling axial-radial circulation in a tank with an axial impeller and radial baffles. The proposed model is based on the analytical solution of the equation for vortex transport in the mean flow of turbulent liquid. The obtained vortex flow model is tested by the results of experiments carried out in a tank of diameter 1 m and with the bottom in the shape of truncated cone as well as by the data published for the vessel of diameter 0.29 m with flat bottom. Though the model equations are expressed in a simple form, good qualitative and even quantitative agreement of the model with reality is stated. Apart from its simplicity, the model has other advantages: minimum number of experimental data necessary for the completion of boundary conditions and integral nature of these data.

scholarly journals Modeling the Excess Velocity of Low-Viscous Taylor Droplets in Square Microchannels

Fluids ◽  
2019 ◽  
Vol 4 (3) ◽  
pp. 162 ◽  
Author(s):  
Thorben Helmers ◽  
Philip Kemper ◽  
Jorg Thöming ◽  
Ulrich Mießner
Keyword(s):  
High Speed ◽  
Process Intensification ◽  
Continuous Phase ◽  
Channel Cross Section ◽  
Optimization Approach ◽  
Mean Flow ◽  
Bypass Flow ◽  
Wall Film ◽  
Proposed Model ◽  
The Mean

Microscopic multiphase flows have gained broad interest due to their capability to transfer processes into new operational windows and achieving significant process intensification. However, the hydrodynamic behavior of Taylor droplets is not yet entirely understood. In this work, we introduce a model to determine the excess velocity of Taylor droplets in square microchannels. This velocity difference between the droplet and the total superficial velocity of the flow has a direct influence on the droplet residence time and is linked to the pressure drop. Since the droplet does not occupy the entire channel cross-section, it enables the continuous phase to bypass the droplet through the corners. A consideration of the continuity equation generally relates the excess velocity to the mean flow velocity. We base the quantification of the bypass flow on a correlation for the droplet cap deformation from its static shape. The cap deformation reveals the forces of the flowing liquids exerted onto the interface and allows estimating the local driving pressure gradient for the bypass flow. The characterizing parameters are identified as the bypass length, the wall film thickness, the viscosity ratio between both phases and the C a number. The proposed model is adapted with a stochastic, metaheuristic optimization approach based on genetic algorithms. In addition, our model was successfully verified with high-speed camera measurements and published empirical data.

scholarly journals Influence of Bottom Topography on Integral Constraints in Zonal Flows with Parameterized Potential Vorticity Fluxes

2013 ◽  
Vol 43 (2) ◽  
pp. 311-323 ◽  
Author(s):  
V. O. Ivchenko ◽  
B. Sinha ◽  
V. B. Zalesny ◽  
R. Marsh ◽  
A. T. Blaker
Keyword(s):  
Potential Vorticity ◽  
Bottom Topography ◽  
Momentum Conservation ◽  
Integral Constraint ◽  
Mean Flow ◽  
Transfer Coefficients ◽  
Flat Bottom ◽  
Zonal Flows ◽  
Eddy Fluxes ◽  
The Mean

Abstract An integral constraint for eddy fluxes of potential vorticity (PV), corresponding to global momentum conservation, is applied to two-layer zonal quasigeostrophic channel flow. This constraint must be satisfied for any type of parameterization of eddy PV fluxes. Bottom topography strongly influences the integral constraint compared to a flat bottom channel. An analytical solution for the mean flow solution has been found by using asymptotic expansion in a small parameter, which is the ratio of the Rossby radius to the meridional extent of the channel. Applying the integral constraint to this solution, one can find restrictions for eddy PV transfer coefficients that relate the eddy fluxes of PV to the mean flow. These restrictions strongly deviate from restrictions for the channel with flat bottom topography.

Alteration of intraaneurysmal hemodynamics by placement of a self-expandable stent

2009 ◽  
Vol 111 (1) ◽  
pp. 22-27 ◽  
Author(s):  
Satoshi Tateshima ◽  
Kazuo Tanishita ◽  
Yasuhiro Hakata ◽  
Shin-ya Tanoue ◽  
Fernando Viñuela
Keyword(s):  
Flow Velocity ◽  
Vortex Flow ◽  
Patient Specific ◽  
Mean Flow ◽  
Single Vortex ◽  
Clinical Images ◽  
The Mean ◽  
Fast Flow ◽  
Mean Flow Velocity ◽  
Flow Stream

Object Development of a flexible self-expanding stent system and stent-assisted coiling technique facilitates endovascular treatment of wide-necked brain aneurysms. The hemodynamic effect of self-expandable stent placement across the neck of a brain aneurysm has not been well documented in patient-specific aneurysm models. Methods Three patient-specific silicone aneurysm models based on clinical images were used in this study. Model 1 was constructed from a wide-necked internal carotid artery–ophthalmic artery aneurysm, and Models 2 and 3 were constructed from small wide-necked middle cerebral artery aneurysms. Neuroform stents were placed in the in vitro aneurysm models, and flow structures were compared before and after the stent placements. Flow velocity fields were acquired with particle imaging velocimetry. Results In Model 1, a clockwise, single-vortex flow pattern was observed in the aneurysm dome before stenting was performed. There were multiple vortices, and a very small fast flow stream was newly formed in the aneurysm dome after stenting. The mean intraaneurysmal flow velocity was reduced by ~ 23–40%. In Model 2, there was a clockwise vortex flow in the aneurysm dome and another small counterclockwise vortex in the tip of the aneurysm dome before stenting. The small vortex area disappeared after stenting, and the mean flow velocity in the aneurysm dome was reduced by 43–64%. In Model 3, a large, counterclockwise, single vortex was seen in the aneurysm dome before stenting. Multiple small vortices appeared in the aneurysm dome after stenting, and the mean flow velocity became slower by 22–51%. Conclusions The flexible self-expandable stents significantly altered flow velocity and also flow structure in these aneurysms. Overall flow alterations by the stent appeared favorable for the long-term durability of aneurysm embolization. The possibility that the placement of a low-profile self-expandable stent might induce unfavorable flow patterns such as a fast flow stream in the aneurysm dome cannot be excluded.

A model for inhomogeneous turbulent flow

1970 ◽  
Vol 317 (1530) ◽  
pp. 417-433 ◽  
Keyword(s):  
Boundary Layer ◽  
Eddy Viscosity ◽  
The Self ◽  
Diffusion Equations ◽  
Mean Flow ◽  
Mean Velocity ◽  
Closed Set ◽  
Law Of The Wall ◽  
The Mean ◽  
Model Equations

A set of model equations is given to describe the gross features of a statistically steady or 'slowly varying’ inhomogeneous field of turbulence and the mean velocity distribution. The equations are based on the idea that turbulence can be characterized by ‘densities’ which obey nonlinear diffusion equations. The diffusion equations contain terms to describe the convection by the mean flow, the amplification due to interaction with a mean velocity gradient, the dissipation due to the interaction of the turbulence with itself, and the dif­fusion also due to the self interaction. The equations are similar to a set proposed by Kolmo­gorov (1942). It is assumed that both an ‘energy density’ and a ‘vorticity density’ satisfy diffusion equations, and that the self diffusion is described by an eddy viscosity which is a function of the energy and vorticity densities; the eddy viscosity is also assumed to describe the diffu­sion of mean momentum by the turbulent fluctuations. It is shown that with simple and plausible assumptions about the nature of the interaction terms, the equations form a closed set. The appropriate boundary conditions at a solid wall and a turbulent interface, with and without entrainment, are discussed. It is shown that the dimensionless constants which appear in the equations can all be estimated by general arguments. The equations are then found to predict the von Kármán constant in the law of the wall with reasonable accuracy. An analytical solution is given for Couette flow, and the result of a numerical study of plane Poiseuille flow is described. The equations are also applied to free turbulent flows. It is shown that the model equations completely determine the structure of the similarity solutions, with the rate of spread, for instance, determined by the solution of a nonlinear eigenvalue problem. Numerical solutions have been obtained for the two-dimensional wake and jet. The agreement with experiment is good. The solutions have a sharp interface between turbulent and non-turbulent regions and the mean velocity in the turbulent part varies linearly with distance from the interface. The equations are applied qualitatively to the accelerating boundary layer in flow towards a line sink, and the decelerating boundary layer with zero skin friction. In the latter case, the equations predict that the mean velocity should vary near the wall like the 5/3 power of the distance. It is shown that viscosity can be incorporated formally into the model equations and that a structure can be given to the interface between turbulent and non-turbulent parts of the flow.

Proposed Model for Optimizing Production System Using CMS

2013 ◽  
Vol 281 ◽  
pp. 673-676 ◽  
Author(s):  
Pawan Kumar Arora ◽  
Abid Haleem ◽  
M.K. Singh ◽  
Harish Kumar
Keyword(s):  
Cell Formation ◽  
Flow Time ◽  
Mean Flow ◽  
Part Families ◽  
Mathematical Mode ◽  
Mean Flow Time ◽  
Proposed Model ◽  
The Mean ◽  
Machine Parts ◽  
Machine Cell

Manufacturing cells are created by grouping the parts that are produced into families. This is based on the operation required by the parts. These cells which consist of machine or workstation are then physically grouped together and dedicated to producing these part families. In this paper a mathematical mode is presented to grouping the machine parts and machine cell. The objective of the proposed model is to minimize the mean flow time and maximize the throughput. This work presents a Genetic Algorithm for the cell formation and part family.Here, the implementation procedure of GA in the CMS problem has been discussed along with the detail of algorithmic parameters used in the algorithm

Measurements of turbulent fluctuations and Reynolds stresses in a tidal current

1956 ◽  
Vol 237 (1210) ◽  
pp. 422-438 ◽  
Keyword(s):  
Tidal Current ◽  
Electromagnetic Flowmeter ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Flat Bottom ◽  
Auto Correlation ◽  
Vertical Scale ◽  
Sea Bed ◽  
The Mean ◽  
The Magnetic Field

Observations have been made of u and w , the horizontal and vertical components of turbulent velocity, in a tidal current, at heights of 50 to 175 cm above the bottom. The measuring instrument was an electromagnetic flowmeter, in which the magnetic field was produced by a. c. at 50 c/s and the p. d. induced in the flowing water was measured by two pairs of electrodes. The measuring head of the instrument was 10 cm in diameter, and two such heads were mounted on a tripod which was laid on the sea bed. The observations were made off Red Wharf Bay, Anglesey, in depths of 12 to 22 m, on a fairly flat bottom consisting mainly of firm sand. For mean currents, U , in the range 25 to 50 cm/s, the r. m. s. values of u were of the order of 10% of U , while those of w were about 6% of U . On a number of records, u and w were recorded simultaneously, and from these the Reynolds stress — ρ [ uw ] was evaluated. At 75 cm above the bottom the values of stress were from 2 to 4 dyn/cm 2 , the corresponding coefficient of correlation between u and w averaging —0·4. Auto-correlation curves and spectrum functions computed from these records showed that u contained considerably more energy in the fluctuations of longer period than w did. Other records were of traces of u or of w at two different heights and showed the smaller vertical scale of w compared with that of u . In the case of u the vertical scale appears to be only about one-third of the scale in the direction of the mean flow.

The influence of jet flow on jet noise. Part 2. The noise of heated jets

1976 ◽  
Vol 73 (4) ◽  
pp. 779-793 ◽  
Author(s):  
R. Mani
Keyword(s):  
Flow Model ◽  
Plug Flow ◽  
Jet Noise ◽  
Jet Flow ◽  
Source Spectrum ◽  
Source Terms ◽  
Mean Flow ◽  
The Mean ◽  
The One ◽  
Heated Jets

This paper continues the study of part 1 into the area of the noise of heated jets. First, this part of the study discusses how a convected wave equation approach based on Lilley's equation leads to additional dipole and simple source terms associated with the velocity fluctuations due to transverse gradients of the mean density of the flow. Once these source terms have been identified and roughly estimated, we revert to a plug-flow model of the jet flow (where now the jet temperature and jet density differ from the ambient values) to estimate the radiation of these singularities. Several novel physical aspects of hot-jet noise are uncovered by the analysis. Indeed the problem of hot-jet noise is the one where the greatest deviations from Lighthill's ideas on jet noise generation are evident. The results are applied to available data and a very satisfactory measure of agreement is obtained with respect to the various predictions of the theory. Mechanisms for ‘excess’ pure jet noise scaling onM6andM4are found to result from the density gradients of the mean flow. The satisfactory agreement with the data suggests a solution of the problem of scaling jet noise with regard to jet temperature effects. The ability to predict correctly the data also suggests that the jet temperature has very little effect on the turbulence source spectrum generating jet noise at least for jet exit velocities up to about 1·5 times the atmospheric speed of sound.

The Characteristics of Spiral Vortex Flow at High Taylor Numbers

1979 ◽  
Vol 21 (2) ◽  
pp. 65-71 ◽  
Author(s):  
M. M. Sorour ◽  
J. E. R. Coney
Keyword(s):  
Vortex Flow ◽  
Hydrodynamic Instability ◽  
Wave Length ◽  
Axial Direction ◽  
Outer Wall ◽  
Mean Flow ◽  
Annular Gap ◽  
Spiral Vortex ◽  
The Mean ◽  
Made In

This experimental investigation is devoted to the study of combined axial and rotational flow in a concentric annular gap, of radius ratio 0.8, formed by a stationary outer and a rotatable inner cylinder. Taylor numbers varying from the critical to an order of 106 will be considered. The investigation is divided into three parts, illustrating different aspects of spiral vortex flow. Firstly, the evolution of the flow with increasing Taylor number at a constant axial Reynolds number is studied by the analysis of the spectrum of the signal from a hot-wire anemometer. Secondly, the wave length and drift velocity of the spiral vortices are determined for the axial direction. Thirdly, the effects of hydrodynamic instability on the mean flow are investigated. It should be noted that the first and second parts are under adiabatic conditions, while the third is both adiabatic and diabatic, heat being transferred isothermally through the outer wall of the annular gap. Also, all of the measurements were made in the fully-developed region of the flow.

The Mean Flow Structure Around and Within a Turbulent Junction or Horseshoe Vortex—Part I: The Upstream and Surrounding Three-Dimensional Boundary Layer

1988 ◽  
Vol 110 (4) ◽  
pp. 406-414 ◽  
Author(s):  
J. D. Menna ◽  
F. J. Pierce
Keyword(s):  
Boundary Layer ◽  
Flow Structure ◽  
Vortex Flow ◽  
Three Dimensional ◽  
Horseshoe Vortex ◽  
Mean Flow ◽  
Complex Flow ◽  
Mean Velocity ◽  
Standard Case ◽  
The Mean

The mean flow structure upstream, around, and in a turbulent junction or horseshoe vortex is reported for an incompressible, subsonic flow. This fully documented, unified, comprehensive, and self-consistent data base is offered as a benchmark or standard case for assessing the predictive capabilities of computational codes developed to predict this kind of complex flow. Part I of these papers defines the total flow being documented. The upstream and surrounding three-dimensional turbulent boundary layer-like flow away from separation has been documented with mean velocity field and turbulent kinetic energy field measurements made with hot film anemometry, and local wall shear stress measurements. Data are provided for an initial condition plane well upstream of the junction vortex flow to initiate a boundary layer calculation, and freestream or edge velocity, as well as floor static pressure, are reported to proceed with the solution. Part II of these papers covers the flow through separation and within the junction vortex flow.

The Mean Flow Structure Around and Within a Turbulent Junction or Horseshoe Vortex—Part II. The Separated and Junction Vortex Flow

1988 ◽  
Vol 110 (4) ◽  
pp. 415-423 ◽  
Author(s):  
F. J. Pierce ◽  
M. D. Harsh
Keyword(s):  
Flow Structure ◽  
Vortex Flow ◽  
Static Pressure ◽  
Horseshoe Vortex ◽  
Cylinder Surface ◽  
Pressure Measurements ◽  
Mean Flow ◽  
Vortex System ◽  
Measured Velocity ◽  
The Mean

The mean flow structure upstream, around, and in a turbulent junction or horseshoe vortex are reported for an incompressible, subsonic flow. This fully documented, unified, comprehensive, and self-consistent data base is offered as a benchmark or standard test case for assessing the predictive capabilities of computational codes developed to predict this kind of complex flow. The three-dimensional turbulent boundary layer-like flow upstream and around the separated junction vortex flow is described in a companion paper, Part I. Part II of these papers covers the flow through the separation region and in the vortex system. This portion of the flow has been documented with mean velocity, static pressure, and total pressure measurements using a very carefully calibrated five-hole probe. The streamwise vorticity field is calculated from the measured velocity field. Extensive floor static pressure measurements emphasizing the region of the vortex system, and static pressure measurements on the cylinder surface are also reported. Flow visualizations on the floor and cylinder surface show unusual detail and agree well both qualitatively and quantitatively with the various flow field measurements.

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