حل عددي پديده‌ي حفره‌سازي روي هندسه‌هاي متقارن محوري با استفاده از روش نسبت حجمي سيال (VOF)

NUMERICAL SIMULATION OF CAVITATION OVER AXISYMMETRIC BODIES USING THE VOLUME-OF-FLUID (VOF) METHOD

در اين تحقيق، پديده‌ي حفره‌سازي روي هندسه‌هاي متقارن محوري حفره‌سازها و بدنه‌ي پرتابه‌ها با استفاده از روش نسبت حجمي سيال (VOF) با الگوريتم يانگز و روش جريان تعادلي همگن به‌صورت عددي مدل‌سازي شده است. كاربرد اصلي روش نسبت حجمي سيال در تحليل جريان‌هاي مايع با سطح آزاد است. در اين تحقيق قابليت حل جريان گاز به الگوريتم VOF افزوده شد و سپس با اعمال مدل‌هاي تحليلي ـ عددي انتقال جرم حفره‌سازي در معادله‌ي انتقال سطح آزاد، پديده‌ي حفره‌سازي شبيه‌سازي شد. نتايج حاصله نشان مي‌دهد كه الگوريتم عددي مورد استفاده، پارامترهاي هندسيِ حفره‌سازي گسترده ــ مانند ابعاد، نحوه‌ي بسته شدن ــ و پارامترهاي جرياني آن ــ مانند ضريب پسا، ضريب فشار، سرعت روي مرز حفره و رفتار جت بازگشتي ــ را با دقت بالايي مدل‌سازي مي‌كند. همچنين ماهيت غيردايمي الگوريتم عددي حاضر امكان مدل‌سازي مشخصه‌هاي رژيم حفره‌سازي ابري، مانند جدايش ساختارهاي بخار از ناحيه‌ي حفره‌، را نيز فراهم مي‌كند.

In this study, transient cavitating flows over 2D-axisymmetric geometries of cavitators and projectile bodies were simulated using the Volume of Fluid (VOF) method and Youngs’ free surface reconstruction algorithm. To predict the shape of the cavity, Navier–Stokes equations, in addition to an advection equation for the liquid volume fraction, are solved. The main application of the Volume of Fluid method is on the simulation of free surface flows. In this work, another capability has been added to the original Volume of Fluid model to solve, simultaneously, the gas and liquid phases. After this step, by applying an analytical-numerical mass transfer algorithm, the cavitation phenomenon has been simulated. The mass transfer between the liquid and vapor is modeled using Kunz’s method. Simulation of the cavitation is based on a homogenous equilibrium flow model. The main features of the developed model compared to available work in the literature are in the use of Youngs’ algorithm to construct the cavity region and in the consideration of surface tension, which becomes important in the prediction of the cavity closure region. The developed model was used for different geometries in a wide range of cavitation numbers from cloud cavitation to a super cavitation regime. The developed numerical model can accurately predict the geometrical parameters of a super cavity, such as its length, diameter, and the closure region. In addition, the flow parameters of a supercavity, such as its drag coefficient, pressure coefficient, and re-entrant jet, were simulated with very high accuracy. The model can also simulate the characteristics of cloud cavitation, such as the separation of large vapor structures from the main cavity region. Totally, the developed model accurately captured the cavity closure region with its transient features of re-entrant jet movement and bubble detachment. In comparison with other available models for cavitation (such as the commercial software, Fluent) the developed algorithm is more efficient and needs far less CPU time and memory.