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1
EN
The classical concept of a homogeneous function is introduced and extended within the theory of differential groups, known in the theory of differential invariants. Invariance under reparametrizations of solutions of partial differential equations is studied. On this basis the wellknown generalizations of the Euler theorem are obtained (the Zermelo conditions). The positive homogeneity concept is then applied to second-order variational equations in field theory.
SK
Standardní koncept homogenní funkce je zaveden a zobecnen pomocí užití diferenciálních grup, známých v teorii diferenciálních invariantu. Studujeme invarianci vzhledem k reparametrizacím integrálních krivek parciálních diferenciálních rovnic. Na základe tohoto prístupu obdržíme známé zobecnení Eulerova teorému, tzv. Zermelovy podmínky. Koncept pozitivní homogenity aplikujeme na variacní rovnice druhého rádu v teorii pole.
2
Content available remote Drążenie elektrochemiczne otworów w elementach silników turbinowych
PL
W referacie przedstawiono zagadnienia chłodzenia łopatek turbin oraz drążenia otworów chłodzących. Rozpatrzono modelowanie matematyczne procesu drążenia elektrochemicznego strugą elektrolitu oraz dobór parametrów obróbki. Wykazano, że należy uwzględniać zmienność przewodnictwa elektrycznego elektrolitu wywołaną wydzielaniem ciepła w procesie. Omówiono badania doświadczalne oraz weryfikację modelu matematycznego.
EN
Electrochemical Jet Machining (ECJM) is used for drilling small holes in aircraft turbine blades and complex shape holes. This paper presents a mathematical model for determining the relationship between the machining rates and conditions of ECJM. Experimental verification is also presented.
EN
The aim of the study was the comparison of different approaches to modeling the injection process in a heavy duty compression ignition engine. The conducted numerical investigation concerned n-hexane direct injection into the engine combustion chamber. Simulations were performed using AVL Fire software, a CFD (Computational Fluid Dynamics) code based on the control volume method. In order to achieve engine conditions, computational model was built basing on piston and cylinder geometry of a real engine and the mesh deformation was defined according to crank mechanism dimensions of the engine. In presented simulations for modeling dispersed phase the Lagrangian approach was used. For capturing the turbulent patterns present in the flow, the Large Eddy Simulation (LES) approach was used. Three different nozzle outflow conditions were compared. In the simplest case, constant flow rate was defined. In the second one, linear stage of increase and decrease of flow rate was defined, and in the third one – the most advanced – data collected during previously done in-injector cavitating flow simulations were used to define the flow parameters on the nozzle outlet. Calculated results for all cases were analyzed and compared. The focus was on the initial stage of the spray. The results show that the way of defining parameters at the outlet influences not only the initial stage of the spray but the whole process.
4
Content available remote Pneumatic actuators with "bouncing" air-jet - part 2: Flow field in the cascade
EN
Unusual actuators generating a fluid force action on a small body by issuing an air jet "reflecting" or "bounding back" from an impact on a wall were described in previous publication (Tesar and Peszynski, 2010). The seemingly impossible return from the wall is based on the unusual effect of the wall provided with perforations that allow a part of the jet to pass through. Upon the impingement, the jet is split in two parts, both having to change their directions. It is the part that remains above the wall, the "reflected" jet, that is of interest for the actuation. In particular, the phenomenon was used in shuttle-less loom to prevent the inserted weft from contact with the reed. The details of the flowfield inside the reed - or cascade of foils with passages between them play a critical role in the phenomenon. This was investigated by flow visualisation discussed in the second part of the paper.
5
Content available remote Pneumatic actuators with "bouncing" air-jet - part 1: Numerical solutions
EN
An actuator generating a force action on a small body by an issuing air jet is based on the unusual, little known and seemingly impossible mechanism of the jet "reflecting" or "bouncing back" from an impact on a solid wall. Under usual conditions the bouncing back from the wall is not possible - the trick is the wall is provided with perforations that allow a part of the jet to pass through. On doing so it has to change its direction and this has to be compensated by the remaining part changing its direction too, into the opposite side as seen from the jet axis. This part forms the "reflected" jet. The phenomenon is investigated by flow visualisation and detailed flowfield computations presented in this paper - the first part of which discusses the computed results.
6
Content available remote Natural liftings of connections to the r-th order bundle
EN
We describe all natural operators A lifting a clasiccal linear connection on an m-dimensional manifold M into a classical linear conection A() on the r-th order frame bundle LrM = invJr/0 (Rm,M).
EN
Hydrographic (towed CTD) and acoustic Doppler current profiler (ADCP) velocity surveys were conducted daily aboard the RV Aranda from July 15 to 26, 1996 at the entrance to the Gulf of Finland, Baltic Sea. Strong alongshore wind forcing that lasted two days caused an intensive downwelling event north of Hiiumaa Island with an approximate 20 m onshore descent of the thermocline. The associated eastward downwelling jet (~30 cm s-1, width 8-12 km) developed into an anticyclonic eddy with a diameter of ~20 km. A strong jet (~35 cm s-1, width 4-6 km) was observed in the periphery of the anticyclonic eddy, centered at the depth of reversal in baroclinicity. The geostrophic streamfunctions were derived from ADCP data and combined with the CTD density field to study the variations of isopycnal potential vorticity. The variation of relative vorticity from -0.95f to 1.2f and five-fold changes in the thickness of the selected isopycnal band caused up to fifty-fold variation of isopycnal potential vorticity over the survey area. The distribution of isopycnal potential vorticity as a conservative property correlated well with the isopycnal salinity distribution. The maximum upward and downward velocities, 35 and 26 m d-1, correspondingly, were estimated through the divergence of the Q-vector using the ω-equation diagnostic technique.
PL
Wykorzystywano prostopadłe zderzanie się dwu płaskich strumieni : gazu i cieczy do intensywnego kontaktowania tych mediów przez mieszanie ich w przepływie o burzliwym mechanizmie i generowania bardzo dużej powierzchni międzyfazowej w rejonie dystrybutora przy dnie reaktora.
EN
Perpendicular collision of two flat jets of the gas and liquid was employed to intense contacting of those media, through mixing them in strong turbulent flow in the region of disperser near the bottom of reactor.
PL
Streszczenie. W artykule przedstawiono wyniki badań pól prędkości w strugach wentylacyjnych rozwijających się w pomieszczeniach o różnej wielkości oraz w sąsiedztwie innych strug. Badania wykazały, że ograniczenie przestrzeni oraz zmiana tła przepływowego zmienia wartość współczynnika rozkładu prędkości - m, a nieznacznie wpływa na położenie bieguna strugi - xa Zmiany wartości współczynnika m wiążą się ze zmianami parametrów turbulentnych.
EN
Air velocity distribution in round jets generated by various types of diffusers is calculated on the basis of the model of free isothermal, axisymmetric jet. In that case, the momentum flux value and two characteristic parameters of the jet, i. e.: velocity distribution coefficient - m and the origin distance - xu are sufficient for the velocity field calculation. The values ofm andxu depend on diffuser type and discharge pattern. In practice jets develop in rooms of various sizes and are affected by walls and entrainment effects. The paper presents the results of experimental tests of jets generated by the same circular nozzle, supplied to enclosures of various sizes and with other surrounding jets. The jet characteristic parameters are determined on the basis of thermoanemometric measurements of the air velocity. Measurement has shown that coefficient - m describing velocity distribution in a jet, depends on the enclosure size as well as on the flow background. This changeability is caused by changes in turbulence intensity - Tu and longitudinal, length, integral scale - Af.
10
Content available remote Intensyfikacja procesów transportu w swobodnych strugach przeciwbieżnych
PL
Praca zawiera wyniki eksperymentalnej analizy pola prędkości w osiowosymetrycznych przeciwprądowych strugach powietrznych. Badaniom poddano wpływ intensywności odsysania czynnika na charakter pola prędkości na osi przepływu. Stwierdzono, iż zastosowanie zewnętrznej strugi koncentrycznej prowadzi do znacznych modyfikacji pola przepływu, a w szczególności do wzrostu intensywności fluktuacji prędkości. Uzyskane wyniki świadczą o możliwości wykorzystania strug przeciwbieżnych do intensyfikacji procesów transportu i zastosowania ich w różnych typach przepływów technicznych.
EN
The paper contains the results of experimental analysis of the velocity field in round countercurrent air jets. The influence of aspiration intensity on the velocity characteristics on the jet centreline was studied. The research revealed significant modifications of the flowfield in the presence of annular reverse flow in particular great increase of turbulence intensity level. The results obtained suggest that the countercurrent jets could for utilised to the improvement of transport processes in a number of practical flow situations.
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