Numerical Simulation of incompressible laminar flow over three dimensional rectangular cavity

Bu çalışmada basit bir geometriye sahip olmasına rağmen oldukça karmaşık bir akım yapısı sergileyen ve gerek askeri gerekse de endüstriyel pekçok uygulamada sıkça karşılaşılan iki veya üç boyutlu kaviteler üzerindeki zamana bağlı, sıkıştırılamaz akış sayısal olarak incelenmiştir. Bu çalışmanın ana amacı, düşük Reynolds sayılarındaki kavite akışı hakkındaki bilgileri ilerletmek ve 3 boyutlu kavite akışı ile 2 boyutlu (2B) veya 3 boyutlu (3B) kavite üzerindeki akımın 3 boyutluluk etkilerini incelemektir. Sayısal çalışmada, Navier-Stokes denklemleri, zamana bağlı, 3B’lu, sıkıştırılamaz bir akış için Fluent ticari yazılımıyla sonlu hacimler yöntemi kullanılarak çözülmüştür ve türbülans modellemesi için de Large Eddy Simülasyonu (LES) yaklaşımı kullanılmıştır. Çalışmada uzunluğunun derinliğine oranı (L/h) 4 olan ve uzunluğunun genişliğine oranı (L/w) 0.8 olan dikdörtgensel bir kavite ele alınmıştır. Yaklaşmakta olan akımın tipi laminer olarak seçilmiştir. Kavite derinliği ve serbest akış hızına göre hesaplanan Reynolds sayısı 4000’dir. LES kullanılarak yapılan sayısal çalışmanın doğruluğu, 2 farklı Re sayısı için (4000 ve 13000) için Özsoy ve diğerleri (2005)’nin yapmış olduğu deneysel çalışma kullanılarak sağlanmıştır. Doğrulama yapıldıktan sonra 2B’lu bir kavite üzerindeki akımın 3B’lu yapısı ile, 3B’lu bir kavite üzerindeki akış yapısı sırasıyla incelenmiştir. Hem 2B’lu hem de 3B’lu kavite akışının içerdikleri akım ayrılması, kayma tabakası, vorteks üretimi, vorteks yayınma mekanizması ve vorteks-duvar etkileşimleri nedeniyle oldukça karmaşık bir yapıya sahip oldukları gözlemlenmiştir. 2B’lu ve 3B’lu çözümlerin kavite orta düzleminde yapılan karşılaştırmaları ortalama akış büyüklükleri cinsinden benzer sonuçlar verse de türbülanslı büyüklükler açısından farklılıklar içerdiği ve özellikle duvara yakın bölgelerde duvar etkisi nedeniyle oldukça farklı bir akış yapısı sergiledikleri gözlemlenmiştir. Anahtar Kelimeler: Kavite akışı, LES, Vorteks, Laminer akım.There are many engineering structures which require some form of cavities on their surfaces in order to perform the task they are designed for. However, these cavities can also be a source of various problems if structures with cavities are subjected to flow conditions. It is well known that the flow over a cavity is a complex phenomenon due to there usually being strong pressure, velocity and sometimes density fluctuations. These in turn can lead to increased drag forces, excessive noise and vibrations problems in structures. It is therefore essential to understand the cavity-flow physics and to be able to model, analyze and predict the outcome of such flows with acceptable accuracy if the adverse effects are to be controlled and minimized. Although many studies have been conducted about the cavity flows most of them have mainly focused on supersonic and compressible flows because of their relevance to aeronautical applications. However, much less attention has been given to very low Mach number cavity flows that are encountered in various grounds, industrial and environmental applications so far. There have been some studies dealing with incompressible cavity flow, but these were mainly focused on flow inside or around two-dimensional cavities and there have been very few investigations on flow inside a three-dimensional cavity. Therefore, there is a real need for better understanding of the three-dimensional effects in cavity flows at very low Reynolds numbers. The main purpose of this work is to study the three-dimensional effects on the characteristics of the cavity flow at very low Mach numbers and to improve the understanding of this type of flow. Therefore this study presents a numerical study into the problem of incompressible laminar flow passing a two and three-dimensional rectangular cavity with a view to understanding the complex nature of the flow and the three-dimensional structure of the cavity. The study is based on the solution of the unsteady, three-dimensional, incompressible Navier-Stokes equations by using finite volume method and Large Eddy Simulation approach. A cavity with length to depth ratio of 4 under an incoming laminar boundary layer is investigated for Re is equal to 4000 (based on cavity depth and free stream velocity). To validate the used computational procedure and simulations, the study of Özsoy et al. (2005) on two dimensional cavities under laminar incoming flow with L/h ratio of 4 is used. After this validation step, three-dimensional flow features of incompressible cavity flows with an incoming laminar boundary layer is investigated. The influence of the recirculating flow inside the cavity on the separated shear layer, the nature of the interactions between the large-scale eddies and the trailing edge corner and the dynamic behavior of the vortex structures occurring in a cavity are studied. The results obtained from computations show that the flow field inside the cavity has a three dimensional structure, even in two-dimensional cavity geometries including vortex shedding mechanism, stretching, wall vortex interaction like clipping or partially escape and so on. Time-averaged parameters in 3D analyses of 3D cavity reveal that the characteristics of the flow change significantly due to the side wall effects. As expected the wall effects are stronger at locations closer to the wall. Another important result from 3D analyses is that if the instantaneous flow field is considered, flow structures are quite different at different stations and highly time dependent. . When 3D flow characteristics are compared to those of 2D it is found that the mean flow features are almost the same for 3D and 2D only at the middle of the cavity. However, this is not the case when the results are compared outside this plane. The 2D and 3D results are significantly different at planes away from the symmetry plane. Although the mean flow quantities are about the same for 2D and 3D in the middle plane, turbulence behavior is quite different. It is believed that the validated computational procedure presented in this study for the analyses of flow over cavities can be used to determine the forces acting to the structures due cavities and this information can also be used for design purposes. Also, the validated computational procedure in this work can help future researchers to perform similar analyses for various kinds of cavities with high level of confidence and to optimize the geometry of the cavities for minimum drag, noise and vibration. Keywords: Cavity flow, vortex, LES, laminar flow.