استفاده از مدل توربولانس بالدوين ـ لوماكس در تحليل جريان چگالشي بخار بين پره هاي يك توربين

AN INVESTIGATION OF CONDENSING STEAM FLOW WITHIN A TURBINE CASCADE USING THE BALDWIN-LOMAX TURBULENCE MODEL

يكي از مشخصه هاي جريان بخار در طبقات انتهايي توربين، انبساط سريع و انحراف از تعادل ترموديناميكي است، به‌طوري كه در شرايط فوق سرد قرار مي گيرد. بازگشت به تعادل با تشكيل ناگهاني قطرات به‌صورت هموژن و رشد تدريجي آنها صورت مي‌پذيرد. در نوشتار حاضر جريان چگالشي بخار با احتساب لزجت به‌صورت دوبعدي، بين پره هاي توربين با استفاده از مدل توربولانس بالدوين ـ ‌لوماكس، شبيه سازي شده است. معادلات جوانه زايي و رشد قطرات با معادلات بقا تركيب، و به‌روش تايم مارچينگ جيمسون حل شده‌اند. به‌اين ترتيب علاوه بر تخمين شوك چگالش، توزيع فشار و نيز اندازه‌ي قطرات با نتايج تجربي مقايسه شده‌اند. از طرفي با احتساب لزجت و لحاظ‌‌كردن توربولانس، اندازه‌ي قطرات در مقايسه با مقادير تجربي بهتر تحقق يافته است. همچنين تعيين ضريب اصطكاك، ضخامت لايه‌ي مرزي و پروفيل‌هاي دوبعدي سرعت نيز ممكن شده است.

One of the characteristics of steam flow in turbine cascades is its rapid expansion and deviation from thermodynamic equilibrium. In this state, the supercoolded steam starts nucleating above the Wilson line and returns to the equilibrium condition due to condensation shock and droplet formation. The release of heat caused by rapid condensation reduces the Mach number, increases the pressure in the supersonic region and affects the aerodynamic behavior of the flow. It is agreed, in the literature, that the nucleating and wet stages of steam turbines are less efficient than those running with superheated steam. In this study, a two-dimensional viscous wet-steam flow in a cascade of turbine blading is simulated, using the Baldwin-Lomax turbulence model, and treated by Jameson’s fourth order Runge - Kutta time marching scheme, which is modified to allow for two-phase effects. The modified classical nucleation theory is employed for modeling nucleation, and the droplet growth equation is obtained based on the mass and energy balance. The system, as a whole, must obey conservation laws. To apply conservation equations to the two- phase flow they have to be combined with nucleation and droplet growth equations and solved simultaneously. An important difference between the two families of equations is that the droplet growth equation is more naturally expressed in Lagrangian rather than Eulerian form, and droplets are assumed to be carried along streamlines that do not necessarily coincide with the grid lines. For this reason, the two sequences of calculations are carried out separately. The, pressure distribution, condensation shock and size of droplets are predicted and compared with empirical results, which show good agreement. By studying the wet-steam flow as viscous and considering the turbulent effects, the prediction of droplet size, in comparison with the experimental results, is improved, and it has become possible to obtain the skin friction coefficient, the boundary layer thickness and the two-dimensional velocity profiles.