Düşük mach sayısında kavite içi akışın aeroakustik incelenmesi
Aeroacoustics investigation of low mach number cavity flow
Yazar: FURKAN COŞGUN
Danışman: DR. ÖĞR. ÜYESİ SERTAÇ ÇADIRCI
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Makine Mühendisliği Ana Bilim Dalı / Makine Mühendisliği Bilim Dalı
Derece: Yüksek Lisans, 2018
Konu: Havacılık Mühendisliği = Aeronautical Engineering ; Makine Mühendisliği = Mechanical Engineering

Özet:
Görece basit bir şekle sahip kavite, birçok mühendislik tasarımında karşılaşılabilir bir geometridir. Kavite akışlarına, askeri ve sivil uçakların iniş takımlarında ve yük mühimmat yuvalarında, otomobillerin kapı oyuklarında, otomobillerin ön ve arka cam boşluklarında, yüksek yapılar etrafındaki akışlarda karşılaşılabilmektedir. Basit bir geometriye sahip olmasına rağmen, kavite boyunca akış, içerisinde bulunduğu tasarım ve çevre için oldukça önemli olumsuz etkiler doğurabilmektedir. Daha yüksek sürtünme kuvvetleri, aşırı seviyelerdeki gürültü ve titreşimler, yapılar üzerinde oluşturduğu yüksek basınç kuvvetleri, kavite akışının sebep olduğu önemli problemlerdir. Örnek vermek gerekirse, uçakların iniş sırasında oluşturdukları gürültü, yükünü bırakmak için yük yuvasını açan uçağın içerisinden bırakılan cismin, kavite akışının, alan içerisinde oluşturduğu güçlü basınç, hız ve yoğunluk değişimlerinden kaynaklı yörüngesinden sapması, en önemli kavite akışı sorunlarından bazılarıdır. 
Kavite ön duvarında oluşmaya başlayan kayma tabakası girdap yapılarının, arka duvar ile etkileşimi, kavite içerisinde ve dışarısında ses basıncı yayılımlarına sebep olmaktadır. Arka duvarından ön duvara doğru ilerleyen ses basınç yayılımı, ön duvarda kayma tabakası ile etkileşmekte, Kelvin-Helmholtz kararsızlığının oluşturduğu akım kopma frekanslarını değiştirmektedir. Bu etkileşim, kayma tabakası kararsızlığını beslemektedir ve kavite rezonanslarının esas sebebini oluşturmaktadır. Bu fenomen Rossiter Mekanizması olarak bilinmektedir. Kendi kendini besleyen kavite salınımları oldukça popüler bir çalışma alanıdır ve hala üzerine çalışılmaya devam edilmektedir. 
Bu çalışmada, düşük Mach sayısında, açık bir kavite boyunca gerçekleşen akış, sayısal olarak incelenmiş ve aeroakustik analizi yapılmıştır. Akustik alan ile akış alanın etkileşimini ifade eden Rossiter mekanizması düşük Mach sayıları için anlaşılmaya çalışılmıştır. Akış, bir kanal içerisindeki kavite geometrisi boyunca gerçekleşmektedir. Doğrulama çalışmalarında kullanılan deneysel konfigürasyona uygun olarak Reynolds sayısı 4000, Mach sayısı ise 0.035'dir. Akış alanı Büyük Girdap Simülasyonu (LES) kullanılarak çözümlenmiş, sayısal sonuçlarımız deneysel veriler ile karşılaştırılarak doğrulanmıştır. Doğrulanan akış alanı içerisindeki kaynak yüzeylerden alınan basınç değerleri akustik analojide girdi olarak kullanılmıştır. Ffowcs Williams-Hawking 
 
denkleminin basitleştirilmiş formu Curle denklemi kullanılarak elde edilen ses basınç değerleri FFT ile frekans alanına geçilmiş, SPL-Frekans spektrumu üzerinden ses seviyeleri incelenmiştir. 
Ayrıca bu çalışmalara ek olarak, kavite akışının sebep olduğu gürültünün azaltılması için 2 tip pasif kontrol metodu uygulanmıştır. Bunlardan ilki, kavite duvarlarına minör ölçülerde eğim verilmesi iken ikinci tip uygulama, kayma tabakasının muhtelif bölgelerine, kare kesitli küt bir cismin yerleştirilmesi olmuştur. Gerçekleştirilen analizlerin sonuçları, akustik ve akış alanı açısından karşılaştırılmış, akustik spektrumlardaki düşüşler veya artışlar incelenmiştir. Analizler ANSYS Fluent ticari yazılım kullanılarak yapılmıştır.

Abstract:
Cavity, whose shape is relatively simple, can be encountered geometry in many engineering applications. Cavity flow can be existing in landing gears and weapon bays of aircrafts, automobile's pillar gaps, flow around the high buildings. Even though cavity has a basic shape, it usually causes some extremely dangerous results not only for design, in which it is exist, but also for environment. Stronger drag forces, high level sound and vibration problems and pressure forces influencing on structures are some problems generated by cavity flows. An additional to these, if an instance too has to be given, while a load is being released from its bay in aircrafts, it can deviate from its orbit because of oscillations generated by cavity flow. These kinds of problems are main reasons why it is important to study onto cavity flows. 
In nature of cavity, free stream approaching cavity interacts with bottom wall and a boundary layer appears. This boundary layer transforms shear layer at leading edge of cavity. Cavity shear layer's vortical structures starting to generate at leading edge of cavity interact with rear Wall. This interaction causes sound pressure propagation inside and outside of cavity. Sound propagation moving from rear wall to leading wall interacts with shear layer at leading edge. This process feds Kelvin-Helmholtz instability and changes frequencies of flow separations. Interaction between sound propagation and shear layer also generates cavity resonances. This phenomenon is known as Rossiter Mechanism. Self-sustained cavity oscillations are quite popular pursuit on which scientists and engineers are studying. 
In this study, low Mach number flow over an open cavity has been investigated numerically. At the same time, it has been investigated in terms of aeroacoustics. Rossiter mechanism, which states interaction between acoustic field and flow field, has been studied to understand better for low Mach numbers. Flow is realized over an open cavity geometry which exist in a channel. According to based experimental study, Reynolds number is 4000 and Mach number is calculated as 0.035. Flow field has been solved using Large Eddy Simulation and Standard k-ω which is a RANS model. Firstly, it has been studied to find mesh independent solution. Five different mesh structures whose coarsest one has one million finite element number in the domain and whose finest one has almost 
 six million finite element number in the domain. During calculation, instant pressure values have been read from a point which is located into the cavity's shear layer region. Time averaged pressure data showed mesh structures after three million, including itself, same results. As a result of this mesh independency study, all other simulation without control and with control has used this mesh structure which has almost 3.5 million cells. Results have been compared and validated with experimental data. It has been shown that LES is superior to RANS in terms of observing instantaneous character of the flow. So that RANS models dissipate all instantaneous behaviours in time line, while LES provide them retain their power without any dissipative effect. Furthermore, it has been highlighted that LES is a requirement for aeroacoustics investigations. Additionally, both of LES and RANS approaches have shown very successful results in validation step with experimental velocity profiles. LES showed again superiority compared to Standard k-ω RANS model. But it was very small difference. Generally, it can be said the fact that if main purpose is to calculate only flow field and to predict only mean flow field. RANS approaches are still enough tools in spite of the fact that there are many developments about DES, LES and DNS which cost expensive computationally in classical understanding. When time averaged pressure field is looked for cavity region, it can be seen that the highest-pressure values have been occurred at rear wall corner because of the fact that shear layer structures impinge at rear wall. This interaction between shear layer and cavity rear wall is main responsible to cavity sound pressure propagation. In the light of this result, cavity rear wall has been determined as sound source in our aeroacoustics analyses. Acoustic Analogy has been used to predict sound pressure values induced interaction between flow and source wall located in flow field. Acoustic Analogy is widely used to predict aerodynamically generated noise due to that it does not require to use very tiny mesh structures and high order discretization schemes, which are very expensive in respect to computational cost. First person, who investigate aerodynamically generated noise, was Lighthill. He derived a non-homogenous wave equation combining Continuity and Momentum equations in 1952. His equation gives very small density perturbations in far field which is induced by turbulence effects occurred in flow field which can be mentioned as near field. Lighthill Analogy is valid only when any solid surface is not available in flow field. It predicts only sounds induced by turbulence effects in flow field that means quadrupole sound source. People who regard effects of solid surface and effects of solid surface motions to aerodynamic sound are respectively Curle, Ffowcs Williams and Hawkings. While Curle equation represents solution of quadrupole and dipole sound sources, Ffowcs Williams and Hawkings equation contains not only quadrupole and dipol effects but also includes monopole terms too. In our study, only dipol term has been calculated. This approach is enough for low Mach number flows and cases which do not include any transient boundary conditions in the domain. Source surface pressure values taken from validated flow field have been used as input in Curle Equation, which is a simplified form of Ffowcs Williams-Hawkings equation. To receive sound pressure values, microphones have been located at 5 different distances. Using sound pressure values, which are taken from Acoustic Analogy, SPL-Frequency spectrums have been plotted with Fast Fourier Transform. By these spectrums, Sound levels in SPL have been investigated and identified. Dominant frequency values have been determined and it has been seen the fact that the most dominant frequency in the spectrum is second peak in higher frequency direction. Second peak in the spectrum has a value of  
300 Hz in frequency. And it shows almost 65 dB for nearest microphone. For furthest microphone, it gives 40 dB level. Comparisons for aeroacoustics resonances have been realized with Rossiter modes. Rossiter had realized his tests for cavity flows which has a Mach number of greater than 0.2 value. It has been being still debated subject that Rossiter Mode empirical formula is valid or not for low Mach numbers. While having made comparison in our study, it has been seen that mode values obtained from Rossiter formula and numerical mode values, they have shown very significant consistency to each other. This result can say us that Rossiter formula is valid for low Mach numbers too like 0.035 value. 
Secondary, two different flow control methods have been realized to supress aerodynamical sound levels induced by interaction between flow and rear wall. One of them has been happened that rear wall is sloped with different angles to weaken power of impingement happening at rear wall. Totally, analyses have been carried out with 5 different rear wall angles. Again, similar mesh structures to what we have used before has been prepared for every different wall angle. Analyses show that giving slope to rear wall in cavity flows decreases impingement power at rear wall region, directly this provides aerodynamical sound reduction in microphones. All angle values have dropped sound levels in all resonances in sound spectrum. But the best results have been acquired in configuration in which 60-degree rear wall slope has been used. This configuration supplies 3 dB reduction in first and third resonance frequencies and provides 1.5 dB drop in second resonance frequency. Other control method, which is used in this study, locating a square barrier into the shear layer generated in cavity leading wall and developing throughout cavity length and consequently interact with rear wall. While first approach has had a purpose to reduce power of interaction or impingement at rear wall intervening rear wall, this has a purpose to reduce power of interaction intervening shear layer development. Giving attention not to create a new source surface, on which high pressure values might happen, a square barrier has been formed with 0.1h edge size where h is representing cavity step height. This square barrier has been located in three different location into the shea layer region. Analyses have been realized with same criteria and approaches used previous numerical simulations. In simulations, it is seen that shear layer generated in leading edge of cavity begins to develop and it becomes unstable at a specific point. So that it can be concluded the fact that barrier located at any upstream location of that specific point provides the best results compared the other barrier configurations. And it can be said the fact that noise level of cavity flow is directly related to vorteks distribution into the cavity gap. If vorteks magnitudes accumulate in near region to rear wall, this may result in bad situations in respect to sound levels. While barrier located at upstream edge gives almost 10 dB sound reduction, barrier located at near edge to rear wall shows a behaviour almost exactly same with main case in sound spectrum. Locating barrier at that specific point gives us a fluctuating point at high frequency region in SPL-Frequency spectrum.         
Finally, results obtained from second control method have a superiority character upon first one. Rossiter formula can be confirmed to use for low Mach number fluid flows. And it can be said the fact that Large Eddy Simulation is a requirement to account acoustic pressure distribution at a receiver compared to Reynolds Averaged Navier – Stokes  
approaches. And additionally, ANSYS Fluent commercial software has been used to carry out numerical simulations and its acoustic module to account sound pressure values.