scholarly journals Theoretical Analyses of the Number of Backflow Vortices on an Axial Pump or Compressor

2020 ◽  
Vol 142 (3) ◽  
Author(s):  
Yu Ito ◽  
Yuhei Sato ◽  
Takao Nagasaki
Keyword(s):  
Outer Region ◽  
Present Theory ◽  
Tip Clearance ◽  
The Other ◽  
Vortex Center ◽  
Mixing Zone ◽  
Axial Pump ◽  
Forced Vortex ◽  
Parameter Ranges ◽  
Theoretical Analyses

Abstract Backflow vortices occasionally occur in the annular mixing zone between the main and axially reverse whirling flows from the impeller tip clearance on an axial pump or compressor. A number (N) of tornado-like backflow vortices rotate around themselves and revolve around the casing axis with a diameter (d) and a revolving angular velocity (ω). To investigate the factors determining N and the movement of the backflow vortices, theoretical analyses are performed. Each backflow vortex is generated in the mixing zone; the core region of each backflow vortex is considered to be a forced vortex, while the outer region is considered to be a free vortex. The ratio (f) of the forced vortex to the distance between the backflow-vortex center and the casing is defined. Each backflow vortex has a circulation and induces movements of all the other backflow vortices depending on the distance between the vortices. The casing restricts the movements of all the backflow vortices, and imaginary image vortices are considered on the other side of the casing. Consequently, for d, ω, N, and f, any parameter can be determined if the other three parameters are specified. As an application of the present theory to an inducer representing an axial pump or compressor, the number (Ncav) of “backflow-vortex cavitations,” which occur around the backflow-vortex center, is predicted. Cavitation is visible; therefore, Ncav is quantitatively measurable. In the parameter ranges studied for the tested inducer, the predicted value of N accurately agrees with the experimentally measured value of Ncav.

Theoretical Analyses of the Number of Backflow Vortices on an Axial Pump or Compressor

2019 ◽  
Author(s):  
Yu Ito ◽  
Yuhei Sato ◽  
Takao Nagasaki
Keyword(s):  
Contact Surface ◽  
Tip Clearance ◽  
The Other ◽  
Vortex Center ◽  
Secondary Vortex ◽  
Axial Pump ◽  
Cylindrical Casing ◽  
Axial Pumps ◽  
Secondary Vortices ◽  
Theoretical Analyses

Abstract This paper presents theoretical analyses of flow fields on an axial pump or compressor, where the main flow enters from one side of the cylindrical casing, whereas an axially reverse and tangentially whirling flow enters from the tip clearance between the casing and the impeller, which sucks in the mixed flow. In this flow field, several secondary vortices exist in the mixing zone across the contact surface between the main and the axially reverse tangentially whirling flow. This type of secondary vortex is called a “backflow vortex.” The backflow vortices are tornado-like, parallel to the casing axis, and periodically distributed on the contact surface; they revolve around the casing axis and rotate around themselves. Regarding the backflow vortices, the relationships between their number (N), revolving diameter (d), revolving angular velocity (ω), and the ratio of the forced vortex region to the distance between the secondary-vortex center and the cylindrical wall (f) were all theoretically investigated. The five major findings are as follows: First, between d, ω, N, and f, any parameter can be determined if the other three are specified. Second, ω decreases, N increases, or f increases when d is increased and the other two are fixed. Third, d decreases, N increases, or f increases when ω is increased and the other two are fixed. Fourth, d increases, ω increases, or f decreases when N is increased and the other two are fixed. Fifth, d increases, ω increases, or N decreases when f is increased and the other two are fixed. To validate these theoretical results, “backflow vortex cavitation,” which occurs around the center of the backflow vortices on a rotating inducer as a representative of axial pumps or compressors, was observed. The backflow vortex cavitation is visible; therefore, d, ω, and N become quantitatively measurable. The test inducer was a triple-threaded helical inducer with a diameter of 65.3 mm and a rotational speed range of 3000–6000 rpm. It was experimentally confirmed that the proposed theoretical analysis is true.

Study on the continuous precipitation of U(IV) oxalate in a vortex precipitator

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Chuanbo Li ◽  
Yongzhi Ning ◽  
Taihong Yan ◽  
Weifang Zheng
Keyword(s):  
Oxalic Acid ◽  
Residence Time ◽  
Nitrate Solution ◽  
The Other ◽  
Nucleation Process ◽  
Average Residence Time ◽  
Continuous Precipitation ◽  
Vortex Zone ◽  
Forced Vortex ◽  
Particles Size Distribution

Abstract The effects of feeding location, stirring speed and apparent average residence time on oxalate crystals size and distribution, tackiness of the product on the walls of reactor and stirring paddle were investigated in a vortex continuous precipitator at 45 °C. The results showed agglomeration happened during nucleation and crystals growth of U(IV) oxalate. Both local supersaturations and agglomeration maked the particles size distribution of U(IV) oxalate from 10–100 µm and the average sizes 35–45 µm. On the other hand, when the nucleation process were controlled to happen in the forced vortex zone, two feeding locations: (a) both oxalic acid and U(IV) nitrate solution into the forced vortex zone, (b) oxalic acid into the free vortex and U(IV) nitrate solution into the forced vortex, tackiness of the crystals on the wall of the precipitator could be effectively avoided.

Annulus Wall Boundary-Layer Measurements in a Four-Stage Compressor

1986 ◽  
Vol 108 (1) ◽  
pp. 2-6 ◽  
Author(s):  
N. A. Cumpsty
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Layer Thickness ◽  
Boundary Layers ◽  
Boundary Layer Thickness ◽  
Tip Clearance ◽  
The Other ◽  
Wall Boundary Layer ◽  
Multistage Compressors ◽  
Full Design

There are few available measurements of the boundary layers in multistage compressors when the repeating-stage condition is reached. These tests were performed in a small four-stage compressor; the flow was essentially incompressible and the Reynolds number based on blade chord was about 5 • 104. Two series of tests were performed; in one series the full design number of blades were installed, in the other series half the blades were removed to reduce the solidity and double the staggered spacing. Initially it was wished to examine the hypothesis proposed by Smith [1] that staggered spacing is a particularly important scaling parameter for boundary layer thickness; the results of these tests and those of Hunter and Cumpsty [2] tend to suggest that it is tip clearance which is most potent in determining boundary-layer integral thicknesses. The integral thicknesses agree quite well with those published by Smith.

scholarly journals VI. An examination into the structure of the cells of the human lungs; with a view to ascertain the office they perform in respiration. By Sir Everard Home, Bart. V. P. R. S. Illustrated by microscopical drawings from the pencil of F. Bauer, Esq. F. R. S

1827 ◽  
Vol 117 ◽  
pp. 58-64 ◽  
Keyword(s):  
Carbonic Acid ◽  
Present Theory ◽  
The Other ◽  
Atmospheric Air ◽  
Acid Gas ◽  
Anatomy And Physiology ◽  
Other Hand ◽  
Human Lungs ◽  
Measure For Measure ◽  
Anatomical Knowledge

No subject connected with physiological enquiry has more excited the attention of the anatomist and chemist, than respiration; but the association between this subject and animal heat, which has so long been supposed to exist, has led to the belief, for the last century, that both enquiries belong more particularly to chemistry than anatomy, and I may probably be considered as going out of my province in taking up this investigation. On the other hand, I see reason to believe that the process of respiration is in itself more simple than is imagined, and more within the reach of disco­very by means of accurate anatomical knowledge of the parts employed, than by means of acquaintance with the intricacies belonging to chemical affinities: I carry this so far as to contend that no explanation of respiration upon chemical principles is to be depended on, unless it accord in all respects with the anatomy and physiology of the lungs , by which the assumed process takes place. The present theory respecting respiration adopted by the chemists, is, that this process decarbonises the blood in the following manner; at every inspiration a compound of oxygen and nitrogen, mixed together, is received into the lungs, and in every expiration, the same volume is returned, measure for measure exactly, with this only difference, that what entered as oxygen is returned in the form of carbonic acid gas, which, according to their theory, proves that no part of the inspired atmospheric air has been retained in the lungs, but a quantity of carbon, equal to that of the oxygen inspired, has been extracted from the blood by the oxygen, making it become carbonic acid gas.

Behavior of Tip Leakage Flow Behind an Axial Compressor Rotor

1986 ◽  
Vol 108 (1) ◽  
pp. 7-14 ◽  
Author(s):  
M. Inoue ◽  
M. Kuroumaru ◽  
M. Fukuhara
Keyword(s):  
Incidence Angle ◽  
Axial Compressor ◽  
Performance Testing ◽  
Tip Clearance ◽  
Vortex Center ◽  
Tip Leakage Flow ◽  
Flow Measurements ◽  
Wall Boundary Layer ◽  
Compressor Rotor ◽  
Work Done

Performance testing and detailed flow measurements were made in an axial compressor rotor with various tip clearances. The experiments were conducted on the condition of the same incidence angle at midspan. Thus, the effect of tip clearance distinguished from that of incidence angle was investigated on the overall performance, work-done factor, blockage factor, and increases in displacement, momentum, and blade-force-deficit thicknesses of the casing wall boundary layer, The phase-locked flow patterns obtained by the multisampling technique show clear evidence of a leakage vortex core behind the rotor. Behavior of the leakage vortex was clarified for various tip clearances by examining loci of the vortex center, decay characteristics of the vorticity at the center, and the total amount of vorticity shed from the blade tip. These results were compared with the leakage vortex model presented by Lakshminarayana.

A note on the time-dependent and the stationary behaviour of a semi-infinite reservoir subject to a combination of Markovian inflows

1971 ◽  
Vol 8 (04) ◽  
pp. 708-715 ◽  
Author(s):  
Emlyn H. Lloyd
Keyword(s):  
Functional Equation ◽  
Explicit Formula ◽  
Generating Function ◽  
Present Theory ◽  
The Other ◽  
Time Dependent ◽  
Independent Sequence ◽  
Time Dependent Solution ◽  
Infinite Reservoir ◽  
Stationary Behaviour

The present theory of finite reservoirs is not rich in general theorems even when of the simple Moran type, with unit draft and stationary discrete independent-sequence inflows. For the corresponding systems with unbounded capacity however there are two classes of results which have been known for some time. One of these classes is concerned with the time-dependent solution, where the theory provides a functional equation for the generating function of the time to first emptiness (Kendall (1957)), and the other with the asymptotic stationary distribution of reservoir contents, for which an explicit formula for the generating function is available (Moran (1959)).

Numerical Simulation on the Electrophoretic Motion of Multiple Particles in Microchannels

2004 ◽  
Author(s):  
Chunzhen Ye ◽  
Dongqing Li
Keyword(s):  
Numerical Simulation ◽  
Flow Field ◽  
Electric Field ◽  
Particle Motion ◽  
Outer Region ◽  
Numerical Results ◽  
The Other ◽  
Double Layers ◽  
Rectangular Microchannel ◽  
Moving Particle

This paper considers the electrophoretic motion of multiple spheres in an aqueous electrolyte solution in a straight rectangular microchannel, where the size of the channel is close to that of the particles. This is a complicated 3-D transient process where the electric field, the flow field and the particle motion are coupled together. The objective is to numerically investigate how one particle influences the electric field and the flow field surrounding the other particle and the particle moving velocity. It is also aimed to investigate and demonstrate that the effects of particle size and electrokinetic properties on particle moving velocity. Under the assumption of thin electrical double layers, the electroosmotic flow velocity is used to describe the flow in the inner region. The model governing the electric field and the flow field in the outer region and the particle motion is developed. A direct numerical simulation method using the finite element method is adopted to solve the model. The numerical results show that the presence of one particle influences the electric field and the flow field adjacent to the other particle and the particle motion, and that this influences weaken when the separation distance becomes bigger. The particle motion is dependent on its size, with the smaller particle moving a little faster. In addition, the zeta potential of particle has an effective influence on the particle motion. For a faster particle moving from behind a slower one, numerical results show that the faster moving particle will climb and then pass the slower moving particle then two particles’ centers are not located on a line parallel to the electric field.

Deposition of Lignin in Differentiating Xylem Cell Walls of Normal and Compression Wood of Buxus microphylla var. insularis Nakai

Holzforschung ◽  
1999 ◽  
Vol 53 (2) ◽  
pp. 156-160 ◽  
Author(s):  
Nobuo Yoshizawa ◽  
Hiromi Ohba ◽  
Junko Uchiyama ◽  
Shinso Yokota
Keyword(s):  
Visible Light ◽  
Cell Walls ◽  
Compression Wood ◽  
Outer Region ◽  
Cell Types ◽  
Deposition Process ◽  
The Other ◽  
Normal Wood ◽  
Long Period ◽  
Buxus Microphylla

Summary The deposition process of lignins within differentiating xylem walls of normal and compression wood of Buxus microphylla var. insularis Nakai was examined by visible-light microspectrophotometry coupled with the Wiesner and Mäule reactions. Buxus formed compression wood on the underside of the leaning stems. The secondary walls of the vessels and fibre tracheids in compression wood showed an intense lignification in the outer region of S2 layer. The spectra of tissues after Mäule and Wiesner reactions showed absorption maxima of around 515 nm and 570 nm, respectively. In differentiating xylem cells of normal wood, lignin composed of both guaiacyl and syringyl units was deposited mainly during the S2 thickening and after formation of the S3 layer in fibre tracheids, whereas in vessels it was actively deposited mainly during the S2 thickening. In compression wood, the deposition of the lignin composed of guaiacyl units was observed for a long period from the early stages of the S2 thickening. Lignification was becoming particularly active at the outer portion of S2 layer after completion of the S2 thickening in both vessels and fibre tracheids. On the other hand, the syringyl units were deposited mainly during the S2 thickening in both cell types.

A New Method to Characterize Dislocation Loops

1994 ◽  
Vol 375 ◽  
Author(s):  
Fuping Liu ◽  
Ian Baker ◽  
Michael Dudley
Keyword(s):  
The Other ◽  
New Method ◽  
Beam Divergence ◽  
Dislocation Loops ◽  
Single Image ◽  
Double Image ◽  
Strain Fields ◽  
X Ray ◽  
White Beam ◽  
Theoretical Analyses

AbstractWhite-beam synchrotron X-ray topography has been used to study the circular, prismatic, [0001] dislocation loops which are commonly-observed on the (0001) plane in polycrystalline, freshwater ice. A new method, involving detailed analyses of the effects of beam divergence on the loop images, has been developed to determine whether a loop is of vacancy or interstitial type. In an 0002 image, one half of a loop (projected as an ellipse) appears as a single image and the other half as a double image. Experimentally, it was found that the 0002 vector drawn from the center of a loop passes through the single image if the loop is of vacancy-type and through the double image if a loop is of interstitial-type. This method of loop characterization was confirmed by performing theoretical analyses of both the dislocation image widths and their strain fields.

Mean momentum balance in moderately favourable pressure gradient turbulent boundary layers

2008 ◽  
Vol 617 ◽  
pp. 107-140 ◽  
Author(s):  
M. METZGER ◽  
A. LYONS ◽  
P. FIFE
Keyword(s):  
Pressure Gradient ◽  
Boundary Layers ◽  
Outer Region ◽  
Present Theory ◽  
Momentum Equation ◽  
Turbulent Boundary Layers ◽  
Momentum Balance ◽  
Physical Layers ◽  
Multi Scale ◽  
The Mean

Moderately favourable pressure gradient turbulent boundary layers are investigated within a theoretical framework based on the unintegrated two-dimensional mean momentum equation. The present theory stems from an observed exchange of balance between terms in the mean momentum equation across different regions of the boundary layer. This exchange of balance leads to the identification of distinct physical layers, unambiguously defined by the predominant mean dynamics active in each layer. Scaling domains congruent with the physical layers are obtained from a multi-scale analysis of the mean momentum equation. Scaling behaviours predicted by the present theory are evaluated using direct measurements of all of the terms in the mean momentum balance for the case of a sink-flow pressure gradient generated in a wind tunnel with a long development length. Measurements also captured the evolution of the turbulent boundary layers from a non-equilibrium state near the wind tunnel entrance towards an equilibrium state further downstream. Salient features of the present multi-scale theory were reproduced in all the experimental data. Under equilibrium conditions, a universal function was found to describe the decay of the Reynolds stress profile in the outer region of the boundary layer. Non-equilibrium effects appeared to be manifest primarily in the outer region, whereas differences in the inner region were attributed solely to Reynolds number effects.

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