بررسي تجربي ساختارهاي پايدار و ناپايدار در پرش هيدروليكي چندضلعي

Experimental Investigation of Stable and Unstable Structures in the Polygonal Hydraulic Jumps

هنگامي كه يك جت عمودي مايع به صفحه‌يي افقي برخورد مي‌كند، اولين انتظاري كه مي‌رود تشكيل يك پرش هيدروليكي دايره‌يي است؛ اما در برخي از سيالات تحت شرايط خاص، انتقال از جريان فوق بحراني به جريان زير بحراني به شكل پرش هيدروليكي چند‌ضلعي پايدار يا ناپايدار نمايان مي‌‌شود. در اين نوشتار علاوه بر پرش‌هاي چند‌ضلعي پايدار، نوعي ديگر از پرش‌هاي چند‌ضلعي نادر كه رفتاري چرخشي ـ موجي از خود بروز مي‌دهند، ارايه شده است. با تعريف ناحيه‌ي ماندگاري براي پرش‌هاي چند‌ضلعي، وابستگي اين ناحيه به اعداد بي‌بعد حاكم مشخص ‌شده است. شعاع متوسط پرش چند‌ضلعي با نظريه‌ي اصلاح‌شده‌ي پرش دايره‌يي واتسون مقايسه ‌شده و مطابقت خوبي حاصل شده است. همچنين تحقيقات آزمايشگاهي انجام شده در اين مطالعه نشان مي‌دهد كه علت ايجاد اين پرش‌ها را مي‌توان به ناپايداري ريلي ـ پلاتو مرتبط دانست.

When a vertical liquid jet impacts on a solid horizontal surface, the first expectation is to have a circular hydraulic jump. However, sometimes the transition from supercritical to subcritical flow occurs in stable or unstable shapes, such as polygons. In this paper, first, the stable polygonal hydraulic jumps are studied. The durability region is defined for the polygonal jumps by experimental observation. The dependency of the durability region on the governing dimensionless groups is determined experimentally. The results show that a polygonal hydraulic jump with several different sides can be created in a certain parameter regime. In this study, in addition to the stable ones, a rare unstable polygonal jump is also presented. This new type of polygonal jump is charactrized by a constant angular velocity. The angular velocity was measured in order to find its relation with the governing parameters of this phenomenon. The results indicate that the angular velocity depends on Reynolds and Weber numbers. The angular velocity of an unstable hydraulic jump can increase or decrease in its durability region by changing the flow rate, downstream height and jet radius. According to the experimental observations, the unstable hydraulic jump has a flow structure similar to type IIb hydraulic jumps that have already been revealed. Afterwards, the jump dimensions are studied by available pictures. The inscribed and circumscribed circular radii of each polygon were measured exactly in order to compare the variable polygons. The observations clearly indicated that the inscribed and circumscribed circles of several polygonal jumps having the same parameter regime have constant radii. Also, the mean jump radius is compared to the modified Watson’s theoretical prediction for the circular hydraulic jump radius. Finally, laboratory studies illustrate that a quick unstable wave appears on the circular jump before the formation of a polygonal form, which may be related to Rayleigh-Plateau instability.