Gemi diesel motorlarının yanma odasındaki akışkan karakteristiklerinin iki boyutlu incelenmesi

Abstract

Bu çalışma da Diesel Motorlarının yanma odasındaki akışkan karakteristiklerini incelenmesi amaçlananmıştır. Çalışmada ilk önce matematiksel modellemeye ilişkin denklemler verilmiştir. Bu denklemlerin çözümü nümerik yolla yapılmaktadır. Çözüme ulaşmak için gerekli olan matematiksel modeller bölüm halinde verilmiştir. Bu amaç için KIVA bilgisayar programı kullanılmıştır. Ek de tablo halinde verilen datalar kullanılarak KIVA bilgisayar programı çalıştırılıp Bölüm 6 de verilen şekillerdeki sonuçlar elde edilmiştir. Bu program zamanla değişen, çok elemanlı, kimyasal reaksiyonlu akışkan dinamiği denklemlerini ve ayrıca buharlaşan akışkan dinamiği denklemlerini çözmektedir. Paket program, özellikle Diesel Motorlar ve direkt püskürtmeli şarjlı motor uygulamaları için geliştirilmiş olup, bu gibi uygulamaları kolaylaştıracak bazı özelliklere sahiptir. Program. Program yapısının çoğu oldukça geneldir. Formüller üç boyutludur ama düzlemsel ve simetrik eksenli iki boyutlu uygulamaları da temin edilebilir. KIVA zaman adımlı ve sonlu farklar metodu kullanarak çözüm yapan bir bilgisayar paket programıdır ve düşük Mach sayılarında verimlilik için akustik altdevre metodunu kullanmaktadır. Diferansiyel denklemleri çözebilmektedir. Köşe yerleşimleri zamanın fonksiyonu olarak belirlenen rasgele seçilen 6 yüzlü parçalardan oluşan genelleştirilmiş bir 3 boyutlu ağ ile uzaysal farlılıklar meydana getirilmektedir. Bu özellik, Lagrangian, Eulerian ve karışık tanımlara imkan tanımakta olup bilhassa kavisli ve hareketli sınırlan tanımlamakta oldukça faydalıdır. Denklemler; kontrol hacmi olarak kabul edilen hücre hacimlerine uygulanır. Hacim üzerindeki integraller yüzey integraline çevrilerek çözülmektedir. Alt şebeke ölçeğinde bir türbülans modeli türbülans enerji transferini de ihtiva etmektedir ve duvar sınır tabaka kanunu da gerçeklenmiştir. Türler ve kimyasal reaksiyonlar için rasgele sayılar vardır. Kimyasal reaksiyonlar kinetik reaksiyonlar ve denge reaksiyonları olarak ikiye bölünerek değişik algoritmalarla işlem görmektedir. Buharlaşan akışkanı temsil için damlaların çarpışma ve birleşme etkilerini ihtiva eden farklı tanecik tekniği kullanılmaktadır. Bir damlacığın yarıçapı gibi geometrik ve diğer benzer özellikleri istatistiki olarak tayin edilmektedir. Akışkan damlacıklar kütle, momentum ve enerji alışverişinde bulunarak birbirlerini etkilemektedir. Bu etkileşimler küçük zaman aralıklarında oluşur. Damlacıkların çarpışmaları ve birleşmeleri dikkate alınmaktadır. Püskürtme ince ve hacim deplasmanlı olduğu varsayılarak kalın püskürtme etkileri ihmal edilmektedir. Geometrik özellikler, başlangıç ve sınır şartlan program için hazırlanan giriş datasında belirtilir. Input Data içinde belirtilemeyen durumlar Fortran diline uygun alt programlar halinde verilebilir. Program bu özelliği sağlayacak durumdadır. Denklemler, nümerik plan ve program yapısı detaylı anlatılmıştır.

Areas of current interest in which reactive flow plays of fündamental role include chemical lasers, industrial buraers and furnaces cent internal combustion engines. With few exceptions, reactive flow problems of practical interest are far too complex to be solved analytically. Quantitative theoretical analyses therefore require the use numerical methods. This study describes the equation which solves the equations of transit multi component chemically reactive fluid dynamics together with those for the dynamics of an evaporating liquid spray. The study is based on the applications to internal combustion engines especially for Marine Diesel Engines. The formulation is spatially two dimensional and encompassed both planer and asymmetric geometry. in the latter case, the flow is permitted to swirl about the axis of symmetry. The code which is used in this study is a time-marching finite difference code that use a partially implicit numerical scheme. Spatial dififerences ALE formed with respect a generalized two dimensional mesh of arbitrary quadrilaterals whose corner locations are specified fünctions of time. This feature allows a Lagrangian, Eulerian ör mixed description and is particularly usefiıl for representing curved ör moving boundary surfaces. Arbitrary numbers of species and chemical reactions are allowed. The latter are subdivided into kinetic and equilibrium reactions, which are treated by different algorithms. The governing equations, numerical scheme are described in Fortran computer language. KIVA code is used in this study and the code is a time marching that solves finite difference approximations to the governing differential equations. The transient solution is marched out in a sequence of finite time increments called cycles ör time steps. Values of the dependent variables on each cycle are calculated from those on the previous cycle. Code is two dimensional vvhich assumes that the dependent variables depend on only two of the three spatial coordinates because of symmetry. The option is provided to select either rectangular ör cylindrical coordinates, corresponding to linear ör axial symmetric, respectively. The velocity component normal to plane of calculation is called the swirl velocity, like the other dependent variables, it is assumed independent of displacement normal is the plane, so that a two dimensional formulation is applicable. The stability limitation of the code is that the fluid cannot traverse more from öne spatial increment per cycle. At low Mach Number the method which is used in the code allows the use of much larger time step flow a prude explicit method. The implicit part of the scheme is solved by a point wise iterative procedure similar to the method of successive över relaxation. Spatial differences are formed with respect to a generalized finite difference mesh ör grid, which subdivides the region of interest into a number of small quadrilateral cells ör zones. The corners of the cells are called the vertices. The positions of the vertices may be arbitrarily specified as functions. of time, thereby allowing a Lagrangian, Eulerian ör mixed description. Since the locations of vertices are arbitrary, the cells are arbitrary quadrilaterals. This type of mesh is called an ALE (Arbitrary Lagrangian Eulerian) mesh and is particularly usefül for representing curved and/or moving boundary surfaces. in determining a method for numerical solution of multi dimensional problems, a fundamentally imported consideration is the relationship between the fluid and the finite grid ör mesh computing zones. Traditionally, there have been two basic viewpoints for both compressible and incompressible flows. The first is Lagrangian in which the mesh of grid points is embedded in the fluid and moves with it. The second known as Eulerian treats the mesh as a fixed reference frame through which the fluid movers. Both the Lagrangian and the Eulerian approaches present advantages and drawbacks. A clear delineation of interfaces and well-resolved details of the flow are afforded by the Lagrangian approach, but it is limited by its inability to çöpe easily with strong distortion which often characterize flows of interest. On the contrary in the Eulerian formulation, strong distortions can be handed with relative ease, but generally at the expense of precise interface defection and resolution of detail. Because of the shortcomings of purely Lagrangian and purely Eularian description techniques have been developed that succeed to a certain extent is combining the best features of both the Lagrangian and Eularian approaches. Öne such technique is the Arbitrary Lagrangian Eulerian (ALE) method in which the grid points may be moved with the fluid in normal Lagrangian fashion ör be held fixed in Eulerian manner ör be moved in some arbitrarily specified way to give a continuos rezoning capability. Because of this freedom İn moving the computational mesh offered by the ALE method, greater distortions in the fluid motion can be handled than would be allowed by a purely Lagrangian method with more resolution than is afforded by a purely Eulerian method. Originally, ALE methods (or numerical solution of the Navier- Stokes equations) have been developed in finite difference formats. The ALE technique proposed that it is applicable to arbitrary finite difference meshes and permits flows at all speeds to be treated. In this study particular emphasis has been placed on giving a comprehensive account the ALE finite volume treatment of unsteady compressible flow problems including the case in which the fluid boundaries involve deforming structures. Mesh description, material, spatial and mixed coordinates: Two basic viewpoint are generally considered in discretizing a fluid region by a finite difference or a finite element method. The first is the Lagrangian in which the mesh or grid points is embedded in the fluid and moves with it; the second knows as Eulerian, treats the mesh as fixed reference flame through which the fluid moves. The Lagrangian description fixed attention on specific particles of the continuum, where as the Eulerian description concerns itself with a particular region of space occupied by the continuum. A representative particle of the continuum occupies a point Po in the initial configuration of the continuum at time t=0 and has the position vector a=(aı,a2,a3) (S.l) The coordinates a, are called the material coordinates. In the deformed configuration, the particle originally at P0 is located at the point P and has the position vector x=(xi,x2,x3) (S.2) The coordinates x; which give the current position of the particle, are called spatial coordinates. The vector u joining the point P0 and P, is the displacement vector. This vector may be expressed ass u=x-a (S.3) In he Lagrangian description, the motion (or flow) of the continuum is expressed in term of material coordinates by equations of the form x^fKM) (S.4) These equations may be interpreted as mapping of the initial configuration of the continuum into its current configuration. On the other hand, in the Eularian XIV description, the motion of the continuum is defined by means of equation (S.4) in terms of the spatial coordinates as a^F^Xj.t) (S.5) The Eulerian description may thus be viewed as one which provides a tracing to its original position of the, particle; that now occupies the location x. The necessary determinant j = |ax1/Sai| (S.6) should not vanish. Since equations (S.4) and (S.5) are: the inverses of one another, any physical property of the continuum that is expressed with respect to a specific particle (Lagrangian description) may also be expressed with respect to the particular location in space occupied by the particle (Eulerian description). For example, if the Lagrangian description of a physical property g is given by g=g(a;,t) (S.7) the Eulerian description is obtained by replacing ai in this equation by the function given in expression (S.5). Thus the Eulerian description of the property g is g = g[F1(x1,t),t] = g*(x"t) (S.8) where the symbol g* is used to emphasize that the functional form of the Eulerian description is not necessarily the same as the Lagrangian form. As already mentioned in the introduction, both the Lagrangian and the Eulerian approaches present advantages and drawbacks and techniques have been developed that succed to a certain descriptions. One such technique is the Arbitrary Lagrangian -Eulerian (ALE) method. The ALE formulation has no basic dependence on particles and treats the computational mesh as a reference frame which may be moving with an arbitrary velocity w in the laboratory system. Depending on the value of the velocity w, the following basic viewpoints may be individuated: XV 1- w=0: The reference frame is fixed in space and this corresponds to the Eulerian viewpoint in which the motion is described in term of spatial coordinates. A particle is identified by the position x (fixed in space) it occupies at time t. 2- w=v, where v is the particle velocity in the laboratory system. Here reference frame moves in space at the same velocity as the particles and this corresponding to the Lagrangian viewpoint. A particle is identified by its initial position vector a time t=0 in the initial configuration of the continuum. 3- w^v^O: The reference frame moves in space at a velocity w which is different both from the particle velocity v and from zero. Such a reference frame is called Arbitrary Lagrangian-Eulerian and any point of it is identified by its instantaneous position vector £. The variables (£;, t) are called the mixed variables. It is emphasized that the position vector ğ is a priori arbitrary and consequently independent from the motion of the particles. In the ALE description, a particle is still identified through its material coordinates aj in the initial configuration of the continuum. However, this identification process is indirect and takes place through the mixed position vector £ which is linked to the material variables (a,, t) by the law of motion of the reference frame. This motion is expressed through equations of the from Si =C(a,,t) (S.9) The ALE description may thus be viewed as a mapping of the initial configuration of the continuum into the current configuration of the reference frame. By analog with expression (S.6), one defines the jacobian j=feM,| (s.io) For the transformation between mixed and material coordinates. The Jacobian j provides a mathematical link between the current volume element dV (function of the mixed variables) in the reference frame and the associated volume element dV0 (function of the material coordinates) in the initial colfiguration: dV=j(a,t)dV0 (S.ll) with j(a,0) = 1 it might be shown (S.8) time rate of change of the mixed jacobian determinant is given by XVI ^U]v.w (S.12) öt The number of species and chemical reactions that can be represented are arbitrary they are limited only by computer time and storage consideration. Chemical reaction are treated by a procedure that distinguishes between slow reactions, which proceed kinematically and fast reactions which are assumed to be in equilibrium. For many applications, all required specifications initial conditions and boundary conditions may be specified using input data alone. This case where the input data is in adequate to define the problem of interest the required specifications may be inserted directly in Fortran from into the appropriate subroutines. The modular structure of the program has been designed to facilitate such modifications. Since the study developed with applications to internal combustion engines especially marine diesel engines. However the basic code structure is modular and quite general and most of the major options (chemical reactions, sprays etc.) can be individually activated or deactivated by setting appropriate valves for the associated input switches.