ارزيابي مدل‌هاي تلاطمي در شبيه‌سازي امواج تيز ايستا در جريان هاي فوق بحراني كانال‌ها

EVALUATION OF TURBULENCE MODELS IN THE SIMULATION OF OBLIQUE STANDING SHOCK WAVES IN SUPERCRITICAL CHANNEL FLOWS

در اين نوشتار معادلات دو‌بعدي متوسط‌گيري شده‌ي عمقيِ سنت ونانت با در نظر‌گرفتن جملات تلاطمي، در جريان فوق بحراني همراه با امواج تيز ايستا حل شده‌اند. براي اين منظور از روش حجم محدود TVD-Roe با استفاده از سلول‌هاي مثلثي بي‌سازمان استفاده شد. براي تكميل معادلات هيدروديناميك، از مدل طول اختلاط (ML)، مدل ، و مدل تنش جبري (ASM) استفاده شد. آنگاه جريان در كانال به همراه يك مانع در پلان با عرض‌هاي متفاوت شبيه‌سازي ‌شد. سپس نتايج عددي حاصله با داده‌هاي به‌دست آمده از مدل آزمايشگاهي مقايسه شد. كاربرد مدل‌هاي مختلف نشان مي دهد كه مد نظر داشتن اثرات تلاطم جواب‌هاي عددي را در محل امواج تيز ايستا بهبود مي‌بخشد. بررسي كيفي نتايج و تحليل كمّي خطاها نشان مي دهد كه جواب‌هاي حاصل از مدل تنش جبري در مقايسه با جواب‌هاي به‌دست آمده از ساير مدل‌ها، مطلوب‌تر است.

In this article, the two-dimensional depth-averaged Saint Venant equations, including the turbulence terms, are solved in a supercritical flow with oblique standing waves, and the effects of several turbulence models on the performance of standing oblique shock waves are investigated. The algorithm applies the finite volume Roe-TVD method with unstructured triangular cells. To avoid spurious oscillations at regions where the gradients of the variable are considerable, advanced slope limiter functions are implemented in the numerical algorithm. The effects of bed slope, bed friction and turbulences are considered in the source terms. The bed slope and bed friction terms are computed using the data at the center of each cell. Three depth-averaged turbulence models, including the mixing length, , and algebraic stress model (ASM), are used to close the hydrodynamic equations. Some experiments are carried out in the flume of a hydraulic laboratory to examine the behavior of the oblique shock waves downstream of a side-baffle. The supercritical flow in the channel is then simulated numerically and results are compared with the experimental data. A comparison of the experimental results and numerical predictions confirm the robustness of the numerical model. In particular, implementation of turbulence models improves the results at the shock positions. Moreover, all of the models are able to simulate the vortex next to the baffle successfully. However, the model and the ASM demonstrate a stronger vortex pattern. Based on our overall findings, the ASM offer superior results to the other models. The quantitative error analysis confirms this finding as well. Our numerical experiments, however, revealed that amongst the source term components, the negligence of the turbulence terms produces the least relative depth error in comparison with the removal of the bed slope or bed friction terms.