Niestateczność ruchu cieczy lepkiej w pofalowanym kanale

• Autorzy: Szumbarski J.

Warianty tytułu

EN

Instability of a viscous liquid flow in a corrugated channel

• Języki publikacji: PL

Abstrakty

PL

Praca dotyczy zagadnień związanych z badaniem niestateczności laminarnego ruchu cieczy lepkiej przez kanał z pofalowanymi ścianami. Celem rozważań jest wykazanie, że pofalowanie poprzeczne (tj. zorientowane prostopadle do kierunku przepływu) o odpowiednio dobranej geometrii prowadzi do radykalnego obniżenia krytycznej liczby Reynoldsa przepływu, przy jednoczesnym zachowaniu oporów hydraulicznych na poziomie podobnym jak w przepływie Poiseuille’a a przez kanał o ścianach płaskich. Wprowadzenie pofalowania poprzecznego wydaje się zatem znacznie lepszym sposobem destabilizacji wewnętrznych przepływów laminarnych przy niskich liczbach Reynoldsa niż stosowane powszechnie pofalowanie wzdłużne. Przepływ bazowy w kanale z poprzecznym pofalowaniem jest wyznaczany przy użyciu semianalitycznej metody zanurzonych granic, co pozwala uniknąć transformacji obszaru. Równania różniczkowe, opisujące ewolucję małych zaburzeń w przepływie, wprowadzono w pełnej ogólności i skonstruowano ich spektralnie zbieżną dyskretyzację. Analizę dynamiki zaburzeń przeprowadzono w dwóch etapach. w pierwszym z nich wyznaczono numerycznie tzw. mody normalne, przeprowadzono obliczenia parametrycznej zmienności modu niestatecznego oraz wyznaczono struktury kinetyczne pola zaburzeń prędkości. W drugiej części analizy zbadano numerycznie wpływ poprzecznego pofalowania na przebieg zjawiska przejściowego wzmocnienia zaburzeń w zakresie podkrytycznych liczb Reynoldsa. pokazano, że poprzeczne pofalowanie ścian nie tylko istotnie modyfikuje wielkość tego wzmocnienia, ale również wprowadza nowy mechanizm wzrostu zaburzeń związany z poprzeczną modelującą profilu prędkości przepływu bazowego. Wykazana w pracy możliwość destabilizacji przepływów wewnętrznych przy niskich liczbach Reynoldsa może być podstawą opracowania nowych metod zwiększania efektywności mieszania i procesów transportu w różnych urządzeniach stosowanych w technice cieplnej, biotechnologii i medycynie.

EN

This work focuses on the problem of the instability of laminar viscous flow in a wavy-walled channel. The aim of the analysis is to show that transversal (i.e., perpendicular in terms of its flow direction) wall waviness can lead to a radical reduction in the critical Reynolds number of the flow, while the hydraulic resistance remains nearly the same as for the Poiseuille flow in the channel with flat walls. Thus, introducing the transversal waviness of the channel walls seems to be a much better way of destabilizing internal laminar flows than the widely used longitudinal waviness. The basic low in the transversely wavy channel is determined by the semi-analytical method of immersed boundaries which allows for the avoidance of any domain transformation. Differential equations describing the evolution of small distubances in the flow have been produced in full generality and their spectrally accurate discretization has been constructed. The analysis of the disturbances dynamics consists of two parts. In the first part, the normal modes have been obtaind numerically, the parametric study of the unstable mode has been performed, and the kinematic structures of the disturbance velocity field have also been described. In the second part, the influence of the transversall wall waviness on the transient amplification of disturbances in the range of subcritical Reynolds numbers has been investigated numerically. It has been show that the wall waviness significantly modifies the amplification magnitude and it also introduces a new mechanism of disturbance growth related to the trasversal modulation of the velocity profile of the basic flow. The possibility of the low-Reynolds-number destabilization of the internal flow could be used as the basis for design of innovative methods of mixing and transport enhancement in various devices in heat technology, biotechnology and medicine.

Słowa kluczowe

PL

niestateczność; ciecz lepka; ruch cieczy lepkiej; kanał pofalowany

EN

instability; viscous liquid; viscous liquid flow; corrugated channel

• Wydawca: Oficyna Wydawnicza Politechniki Warszawskiej
• Czasopismo: Prace Naukowe Politechniki Warszawskiej. Mechanika
• Rocznik: 2007
• Tom: z. 218
• Strony: 3--171
• Opis fizyczny: Bibliogr. 121 poz., rys., tab., wykr.

Twórcy

autor

Szumbarski J.

• Wydział Mechaniczny Energetyki i Lotnictwa

Bibliografia

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