التفاصيل البيبلوغرافية
| العنوان: |
Sanki-bir-boyutlu kavitasyonlu daimi lüle akışı çözümlerinin kararlılığı. (Turkish) |
| Alternate Title: |
Temporal stability of steady-state quasi-one-dimensional bubbly cavitating nozzle flow solutions. (English) |
| المؤلفون: |
PasĠnlĠOĞlu, ġenay, Delale, Can Fuat |
| المصدر: |
ITU Journal Series C: Basic Sciences; Nov2010, Vol. 8 Issue 1, p97-108, 12p, 6 Graphs |
| مصطلحات موضوعية: |
CAVITATION, FLUID dynamics, NOZZLES, BUBBLE dynamics, AERATED water flow, RAYLEIGH model, RAYLEIGH flow, DAMPING (Mechanics), STABILITY (Mechanics), NUCLEATION |
| Abstract (English): |
Cavitating flows through converging-diverging nozzles seem to be the simplest configurations for analysis in hydrodynamic cavitation. They have direct applications in cavitation in ducts and venturi tubes as well as in Diesel injection nozzles. The first model of bubbly liquid flow through a convergingdiverging nozzle was proposed by Tangren etal. (1949) using a barotropic relation. The problem was reconsidered by Ishii et al. (1993) by taking into account unsteady effects, but still neglecting bubble dynamics. A summary of barotropic models can be found in the book by Brennen (1995). For cavitating flows it is essential to consider bubble dynamics together with the equations of nozzle flow. A continuum bubbly mixture flow model that couples spherical bubble dynamics, as described by the classical Rayleigh- Plesset equation, to the flow equations was proposed by van Wijngaarden (1968). Steady-state solutions of bubbly cavitating flows through converging- diverging nozzles have been investigated by Wang and Brennen (1998) and by Delale etal. (2001) using the continuum bubbly liquid flow model. Assuming that the gas pressure inside the bubble obeys the polytropic law and lumping all damping mechanisms, in a crude manner, by a single damping coefficient in the form of viscous dissipation, both investigations have demonstratedbifurcation of steady-state solutions to flashing flow instabilities by varying the inlet void fraction (or inlet bubble radius orinlet cavitation number). A numerical investigation of unsteady bubbly cavitating flows in converging- diverging nozzles on the same model has been carried out by Preston etal. (2002). They show that the instabilities encountered in the steady-state solutions of quasi-one dimensional bubbly nozzle flows may correspond to unsteady bubbly shock waves formed in the diverging section of the nozzle and propagated downstream. The aim of this investigation is to present a detailed analysis of quasi-one-dimensional unsteady bubbly cavitating flows in converging- diverging nozzles with the inclusion of bubble/bubble interactions as discussed in Delale etal. (2001). The description is, therefore, restricted solely to the investigation of the interplay between the overall compressibility of the continuum bubbly mixture and flow unsteadiness. Although the stability of both inviscid and viscous bubbly parallel flows have been investigated by d'Agostino etal. (1997) and d'Agostino and Burzagli (2000), it is important to investigate the temporal stability of cavitating nozzle flows in the quasi onedimensional approximation to find out whether such steady-state solutions are stable with respect to temporal perturbations. In this study the stability of steady-state bubbly cavitating nozzle flows is considered. For this reason, quasi-one-dimensional unsteady bubbly cavitating nozzle flows are considered by employing a homogeneous bubbly liquid flow model together with the nonlinear dynamics of cavitating bubbles, described by a modified Rayleigh-Plesset equation. Nucleation, coagulation of bubbles and bubble fission are neglected. The various damping mechanisms are lumped together by a single damping coefficient in the form of viscous dissipation. A polytropic law for the expansion and compression of the gas inside the bubble is assumed. The initial distributions, inlet conditions and nozzle geometry are choosen such that cavitation can occur in the nozzle. Under these assumptions the complete system of equations, by appropriate uncoupling, are reduced to two evolution equations, one for the flow speed and the other for the bubble radius. The evolution equations for the bubble radius and flow speed are then perturbed with respect to flow unsteadiness resulting in a coupled system of linear partial differential equations for the radius and flow speed perturbations. This system of coupled linear PDE's is then cast into an eigenvalue problem. The eigenvalues for the resulting system are found by normal mode analysis in the inlet region of the nozzle where the coefficients of the system of the PDE's are almost constant. Stability diagrams are obtained by varying the various flow parameters (cavitation number, etc.) against the perturbation wave number k. Results found show that the steady-state bubbly cavitating nozzle flow solutions are temporally stable only for perturbations with very small wave numbers. The effect of damping mechanisms on the stability of the steadystate solutions seems to be negligible in the inlet region because of the very small growth rate of the bubbles. The stable regions of the stability diagram for the inlet region of the nozzle are seen to be broadened by the effect of turbulent wall shear stress. [ABSTRACT FROM AUTHOR] |
| Abstract (Turkish): |
Bu çalışmada, yakınsak-ıraksak bir lülede sanki-bir-boyutlu kavitasyonlu daimi kabarcıklı akış çözümlerinin, kabarcık/kabarcık etkileşmeleri de göz önünde bulundurularak zamana göre kararlılığı incelenmiştir. Bunun için homojen kabarcıklı sıvı akışı modeli kullanılarak sanki-bir-boyutlu daimi olmayan kavitasyonlu lüle akış denklemleri kabarcık dinamiği yasasıyla birlikte (iyileştirilmiş Rayleigh- Plesset denklemi) gözönünde bulundurulmuştur. Çekirdekleşme, kabarcık bölünme ve birleşmeleri ihmal edilmiştir. Tüm sönüm mekanizmaları, viskoz yutulma biçiminde tek bir sönüm katsayısıyla ele alınmış, kabarcıkların büyüme ve büzülmelerinde kabarcık içindeki gaz için politropik yasa kullanılmıştır. Başlangıç dağılımları, giriş koşulları ve lüle geometrisi, lülede kavitasyon oluşacak şekilde alınmıştır. Bu varsayımlar altında, model denklem sistemi, akış hızı ve kabarcık yarıçapı için iki evrim denklemine indirgenmiştir. Evrim denklemleri, daimi olmayan akışa göre pertürbe edilerek kabarcık yarıçapı ve akış hızı pertürbasyonları için kuple lineer kismi diferansiyel denklem sistemi elde edilmiştir. Bu kuple lineer denklem sistemi genelleştirilmiş özdeğer problemine dönüştürülmüş ve lülenin belli bölgeleri için özdeğerler hesaplanmıştır. Özdeğer problemindeki denklem sisteminin tüm katsayılarının hemen hemen sabit olduğu lüle giriş bölgesinde, normal mod analizi yöntemiyle problem kesin olarak çözülmüştür. Çeşitli akış parametrelerinin (kavitasyon sayısı, vs.) k pertürbasyon dalga sayısıyla değişimi için kararlılık diyagramları elde edilmiştir. Elde edilen sonuçlar, kavitasyonlu daimi lüle akışı çözümlerinin sadece çok küçük dalga sayıları için zamana göre kararlı olduğunu göstermiştir. Lüle giriş bölgesi için kararlılık diyagramlarındaki kararlı bölgelerin, türbülanslıcidar kayma gerilmesi etkisi gözönünde bulundurulduğunda genişlediği görülmüştür. [ABSTRACT FROM AUTHOR] |
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