acoustical cavitation and bubble dynamics

... Theory and Numerical Analysis, North-Holland Publ Co., Amsterdam, 1984. [33] R Temam and M Ziane , Some mathematical problems in geophysical fluid dynamics, in Handbook of Mathematical Fluid Dynamics, ... Functional spaces and inequalities Denote by L2(Ω), L2(M ) and H m (Ω), H m (M ) the usual L2-Lebesgue and Sobolev spaces, respectively ([1]).Let Trang 8Definition 1 Let v0∈ V1 and T0∈ V2, and letT be ... coupled to thermodynamics and salinity diffusion-transport equations,which account for the buoyancy forces and stratification effects under theBoussinesq approximation Moreover, and due to the shallowness...

Ngày tải lên: 06/03/2014, 08:21

... Trang 1 CAVITATION AND BUBBLE DYNAMICS by Christopher Earls Brennen OPEN © Oxford University Press 1995 Also available as a bound book ISBN 0-19-509409-3 Trang 2CAVITATION AND BUBBLE DYNAMICSby ... recent text by Carey (1992) and to the reviews by Blake (1949), Bernath (1952), Cole (1970), Blander and Katz (1975), and Lienhard and Karimi (1981) We present here a brief and simplified version ... Viscous Effects in Cavitation Inception 1.15 Cavitation Inception Measurements 1.16 Cavitation Inception Data 1.17 Scaling of Cavitation Inception References Trang 32.3 Bubble Contents2.10...

Ngày tải lên: 24/04/2014, 16:46

... Earls, Cavitation and bubble dynamics / Christopher Earls Brennen 1941-p.cm.—(Oxford engineering science series; 44)Includes bibliographical references and index Cavitation and bubble dynamics ... TRAVELING BUBBLE CAVITATION 218 7.3 BUBBLE/FLOW INTERACTIONS 219 7.4 EXPERIMENTAL OBSERVATIONS 220 7.5 LARGE-SCALE CAVITATION STRUCTURES 227 7.6 VORTEX CAVITATION 227 7.7 CLOUD CAVITATION ... recent text by Carey (1992) and to the reviews by Blake (1949), Bernath (1952), Cole (1970), Blander and Katz (1975), andLienhard and Karimi (1981) We present here a brief and simplified version ofhomogeneous...

Ngày tải lên: 11/06/2014, 10:33

... calculations have since been carried out by Ivany and Hammitt (1965), Tomita and Shima (1977), and Fujikawa and Akamatsu (1980), among others Ivany and Hammitt (1965) confirmed that neither surface ... ether bubble in glycerine before (left) and after (center) a collapse and rebound The cloud on the right is the result of a succession of collapse and rebound cycles Reproduced from Frost and ... side and this results in the development of a high-speed re-entrant microjet which penetrates the bubble Such microjets were first observed experimentally by Naude and Ellis (1961) and Benjamin and...

Ngày tải lên: 07/08/2014, 10:20

... 47, 283 290 ● Plesset, M.S and Prosperetti, A (1977) Bubble dynamics and cavitation Ann Rev Fluid Mech., 9, 145 185 ● Prosperetti, A and Lezzi, A (1986) Bubble dynamics in a compressible liquid ... boundary layer effects on cavitation inception and on traveling bubble cavitation are reviewed by Holl (1969) and Arakeri (1979) Rayleigh-Plesset models of traveling bubble cavitation that attempted ... the early (and classic) observations of individual traveling cavitation bubbles by Knapp and Hollander (1948), Parkin (1952), and Ellis (1952) make mention of the deformation of the bubbles by...

Ngày tải lên: 07/08/2014, 10:20

... effects of bubbles in cavitating flows and the role played by bubble dynamics in homogeneous flows 6.8 ACOUSTICS OF BUBBLY MIXTURES Trang 5One class of phenomena in which bubble dynamics can ... (1945) and Carstensen and Foldy (1947) applied the classical acoustical approach and treated the problem of multiple scattering by randomly distributed point scatterers representing the bubbles ... considered constant and α1, τ1 =4πR 1 /3, and η are the void fraction, individual bubble volume, and population of the mixture far upstream Substituting for ρ in the equation of motion and integrating,...

Ngày tải lên: 07/08/2014, 10:20

... terms u j∂u i /∂x j are not identically zero on the surface of the bubble More recently Proudman and Pearson (1957) and Kaplun and Lagerstrom (1957) showed that Oseen's solution is, in fact, the ... observed and measured by Young, Goldstein, and Block (1959) and others Finally, we should comment on a related effect caused by surface contaminants that increase the surface tension When a bubble ... limit the terms on the left-hand side of Equation 5.2 are neglected and the viscous term retained This solution has the form (5.11) Trang 4(5.12) (5.13) where A and B are constants to be determined...

Ngày tải lên: 07/08/2014, 10:20

... translation of cavitation bubbles near walls Here the motivation is to understand the development of impulsive loads on the solid surface (see Section 3.6), and therefore the primary focus is on bubbles ... ellipsoidal bubbles that may oscillate in shape and have oscillatory trajectories (Hartunian and Sears 1957) As the bubble size is further increased to the point at which We≈20, the bubble acquires ... right-hand sector of the graph is characterized by large relative motion, as suggested by Equation 5.98 The quasistatic regimes for WR/ν » 1 and WR/ν « 1 are in the lower right- and left-hand ...

Ngày tải lên: 07/08/2014, 10:20

... broader and longer the cavity becomes and the lower the drag coefficient For a finite tunnel width, there is a critical cavitation number, σc , at which the cavity becomes infinitely long and no ... (Wu, Whitney, and Brennen 1971) In this sense the Riabouchinsky and open-wake models bracket the real flow 3 The ``reentrant jet'' model, which was first formulated by Kreisel (1946) and Efros (1946), ... the smooth detachment point These circumstances and this condition were first recognized independently by Brillouin (1911) and by Villat (1914), and the condition has become known as the Brillouin-Villat...

Ngày tải lên: 07/08/2014, 10:20

... but Re{ } and Re{ } tend to zero, and these two nonzero coefficients tend to the quasistatic values of dC L /dα and dCM /dα, namely π/2 and 5π/32, respectively Trang 9Figure 8.29 Real and imaginary ... attack (for a fixed cavitation number) is presented in Figure 8.22 Also shown in this figure are the lines of •=4/3 in the supercavitation solution and •=3/4 in the partial cavitation solution ... from the partial cavitation model of Acosta (1955) (dashed lines) and the supercavitation model of Tulin (1953) (solid lines) as a function of angle of attack, α, for several cavitation numbers,...

Ngày tải lên: 07/08/2014, 10:20

... the first (bubble 1) and the second (bubble 2), and the first and the third (bubble 3) bubbles are 66.7 μs and 267 μs respectively Bubble 1 has collapsed, while the others are still expanding The ... resultant bubbles, and the lower bubble’s jet penetrates bubble 3 which top surface is elongated towards bubble 1 Bubble 2 gets very close to bubble 3, forming a ‘mushroom-shaped’ bubble (Frame ... (Adikhari, 2006)) Bubble 1 and 3 are created 25 μs after bubble 2 The center bubble 2 enters its collapse phase while bubble 1 and 3 are still expanding Being much flattened on both the top and bottom...

Ngày tải lên: 12/09/2015, 08:19

... and we break down the results into banking groups and years Over the whole period 2005-2009 and over all banking groups, the median bank earned26.3 basis points (in relation to total assets and ... Faktor f¨ur die H¨ohe des Zins¨anderungsrisikos bewegt sich im Einklang mit derZinsstrukturkurve 2 Auf der Ebene der Einzelbank wird die zeitliche ¨Anderung desZins¨anderungsrisikos aber weitgehend ... transformation, and the dynamics of the termstructure1 1 Introduction For many banks, term transformation represents a substantial part of their interest income.This is especially true of small and medium-sized...

Ngày tải lên: 16/02/2014, 06:20

... appear [40] H Hofer and E Zehnder, Symplectic Invariants and Hamiltonian Dynamics, Birkhăuser, a Basel, 1994 [41] F Lalonde and D McDuff, J-curves and the classification of rational and ruled symplectic ... three-spheres and Hamiltonian dynamics By H Hofer, K Wysocki, and E Zehnder* Annals of Mathematics, 157 (2003), 125–257 Finite energy foliations of tight three-spheres and Hamiltonian dynamics By ... Princeton, NJ, 1973 [48] T H Parker and J G Wolfson, Pseudo-holomorphic maps and bubble trees, J Geom Anal (1993), 63–98 [49] J W Robbin and D Salamon, The spectral flow and the Maslov index, Bull London...

Ngày tải lên: 05/03/2014, 23:20

... the cavitation bubbles), instead of heating the whole system This provides localized, highly extreme reaction conditions II PHYSICAL AND CHEMICAL PRINCIPLES A Acoustical Cavitation and Bubble Dynamics ... balloon and the higher is the intensity This continues until cavitation begins Cavitation produces bubbles, and sound in a solution cannot pass unaffected through a region of bubbles The bubbles ... rectified diffusion, and is also applicable to the dissolved gases and volatile solutes, which can be concentrated in stable cavitation bubbles during many cycles A slow-growing cavitation bubble will...

Ngày tải lên: 11/08/2014, 13:21

... Nyamukapa CA, Mason PR, Garnett GP, Chandiwana SK, Foster G, Anderson RM: Impact and process evaluation of integrated community and clinic-based HIV-1 control: a cluster-randomised trial in eastern Zimbabwe ... pre-intervention (control) and two post-intervention health units were selected per district, and the sample included nine dispensaries, three health centres and four hospitals Three scenarios and checklists ... sessions), and 221 in Round using Manual (nine sessions) Questionnaires were available from 208 (100%) (pre) and 203 (98%) (post) health workers trained in Round 1, and from 221 (100%) (pre) and 221...

Ngày tải lên: 20/06/2014, 08:20

... Bronchitis (thousand cases, adults) Respiratory Hospital Admissions (thousands) Cardiac Hospital Admissions (thousands) Restricted Activity Days (thousands) Respiratory medication use (thousand days, ... from Table and Table Country Austria Belgium Cyprus Czech Rep Denmark Estonia Finland France Germany Greece Hungary Ireland Italy Latvia Lithuania Luxembourg Malta Netherlands Poland Portugal ... from Table and Table Country Austria Belgium Cyprus Czech Rep Denmark Estonia Finland France Germany Greece Hungary Ireland Italy Latvia Lithuania Luxembourg Malta Netherlands Poland Portugal...

Ngày tải lên: 23/03/2014, 00:20

... Amaroo and Reiziq (medium-grain) Paddy samples were dried at 40, 60, and 80oC and then tempered for 0, 40, 80 and 120 The dried rice samples were then stored up to four months at 4, 20 and 38 ... compact-drying system and to validate molecular relaxation concept during post-drying annealing and subsequent storage of rice To organise training workshops and demonstrations for the farmers and extension ... harvesting and milling losses and degradation of rice quality To increase the research and teaching capabilities of institution and staff members on rice quality and related products To build...

Ngày tải lên: 22/06/2014, 12:20

... use of branding for products People have historically used ideology as a way of labeling both themselves and politicians, and then making a connection between themselves and the candidate and/ or ... invaders, to abolish the colonial and feudalist regime, to liberate and reunify the country, and then carry out the cause of renovation and socialist construction and firmly defend national independence." ... exchanges between political entities and their environment and among themselves with particular reference to the position of those entities and their communications‖ And ―the practice of political...

Ngày tải lên: 26/03/2015, 08:59

... orchestra, jazz band, old-time band, and various lecture series; and NIU’s and Rockford College Music Academy student and faculty performances and participation in the Rockford Symphony and other musical ... acquisition, and marketing, e.g., entrepreneurship training and assistance providing customized research and data procuring grants which support current business and industry providing conference and ... and supporting apprenticeship programs, and convening and being responsive to advisory committees with representatives from business and industry Once needs are identified, higher education and...

Ngày tải lên: 17/03/2014, 07:20

... business and liquidity, and of short-term developments of demand and supply in the specific sectors and markets where enterprises operate Investment financial institutions, on the other hand, develop ... key players in recapitalization of banks; in Poland and Hungary foreign banks brought much needed know-how and capital; and in Argentina and New Zealand, foreign banks also brought fresh capital ... entry and sanctioning criteria, and ban discriminatory and unfair practices Government should also ensure that SRO rules and operations are not detrimental to small participants and consumers, and...

Ngày tải lên: 24/10/2012, 09:33