Kanat profili üzerinde oluşan buzun iki boyutta matematiksel modellenmesi ve sayısal çözümü
Two dimensional mathematical modelling and numerical solution of accumulated ice on wing profiles
Yazar: RAMAZAN DÖKME
Danışman: PROF. DR. AHMET CİHAT BAYTAŞ
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Uçak ve Uzay Mühendisliği Ana Bilim Dalı / Uçak ve Uzay Mühendisliği Bilim Dalı
Derece: Yüksek Lisans, 2019
Konu: Uçak Mühendisliği = Aircraft Engineering

Özet:
Ses altı uçan hava araçlarının uçuş esnasında veya öncesinde kontrol yüzeyleri üzerinde oluşabilecek buz katmanı, uçuş performansını olumsuz etkilenmesine yol açmaktadır. Bu performans kaybı kuyruk ve kanat gibi kontrol yüzeylerinde kontrol kabiliyetinin azalması, tamamen kaybolması, ağırlık artışına neden olurken, motor girişleri gibi yerlerde oluştukları yerlerden koparak yapısal hasarlara da neden olarak uçuş emniyetinde önemli bir risk artışına sebebiyet vermektedir. Diğer yandan yakıt sarfiyatını artırdığından ticari olarak büyük boyutlarda maliyetlere neden olmaktadır. Havacılığın ilk yıllarından itibaren buzlanma oluşumu sürekli olarak araştırılan bir konu olmakla beraber günden güne geliştirilmektedir. Bu gelişim daha çok matematiksel modellerde ve bu modellerin neticesinde ortaya çıkartılan simülasyon programlarında yaşanmaktadır. İlk olarak  buzlanma analiz metotları NASA himayesinde yapılmıştır. Ardından Fransa ve İngiltere'deki havacılık şirketleri arasındaki iş birlikleri ile uçuş test ve buzlanma simülasyon kodlarında alternatifler ortaya çıkartılmıştır. Hava aracı buzlanma simülasyon programlarının sertifikasyonu ve hava araçlarının uçabileceği buzlanma koşulları FAA ve EASA havacılık otoriteleri tarafından tanımlanmaktadır.Sertifikasyon gereksinimlerini karşılaması açısından uçuş testleri, rüzgar tüneli testleri ve sayısal çözüm gibi yöntemlerden faydalanılmaktadır. Sertifikasyon ihtiyaçlarının karşılamasının yanı sıra buzlanmayı önleyici, buzlanmayı giderici sistemlerin tasarımında uçak yüzeyinde buz kütlesi ve limit değerlerinin bilinmesine ihtiyaç duyulmaktadır.

Uçak buzlanması çalışmalarındaki ortak tanımlamalara göre kırağı (rime) ve şeffaf (glaze) olmak üzere iki çeşit buzlanma türü vardır. Hava içindeki su damlacıklarının çok düşük sıcaklıktaki yüzey üzerinde hızlı şekilde birikmesiyle genellikle beyaz renkte olan kırağı buzlanması görülmektedir. Kırılgan olduğundan oluştuğu yüzeyden uzaklaştırılması kolaydır. Şeffaf buz ise donma sıcaklığının yakınlarında çarpan su damlacıklarının bir kısmının donmasıyla ortaya çıkmaktadır. Oldukça sert yapısı ve düzgün olmayan şekilleri nedeniyle hava araçları üzerinde en fazla olumsuzluğa neden olan buz oluşum türüdür. Buz oluşumunu etkileyen en önemli parametreler sıcaklık $T_{\infty}$, damlacık boyutu $d_{p}$, serbest akış hava hızı $V_{\infty}$, damlacıkların birim hava hacmi içinde bulunma miktarı $LWC$ ve yerel ve genel çarpma verimi $\beta$'dır. Çarpma verimi diğer parametrelerden farklı olarak buzlanmanın oluşacağı geometri (veter uzunluğu, silindir çapı) boyutuna bağlı olarak direkt $\beta$'yı etkilemektedir. Geometri boyutu büyüdükçe çarpma verimi $\beta$ düşmekte ve daha az buz katmanı oluşumu görülmektedir. Buzlanma kaynaklı kazaların daha çok küçük uçakların yüzeylerinde yaşanmasının temel sebeplerinden biri bu boyut etkisi açıklamaktadır.

Hava araçlarındaki buzlanma probleminin çözümü için yapılan çalışmalarda olduğu gibi bu çalışmada da kanat, kuyruk ve silindir geometrileri üzerinde buzlanma simülasyonu yapacak olan bilgisayar programı geliştirme amaçlanmıştır. Çalışma sırasında Fortran, Techplot ve GetGraph Digitizer yazılımları kullanılmıştır. Buzlanma simülasyon programı FORTRAN programlama dilinde yazılmış olup alınan sonuçlar literatürdeki sonuçların GetGraph Digitizer programı yardımıyla Techplot programında aynı anda grafik üzerinde karşılaştırılmıştır. Buzlanma simülasyon bilgisayar programı panel yöntemi ile akış alanı çözümü, Lagrange yaklaşımı ile damlacık yörünge ve birikme etkinliği hesaplamaları, termodinamik analiz ve genişletilmiş Messinger Modeli ile buz birikim hesabı olmak üzere dört ana kısımdan oluşmaktadır. Mevcut çalışmadaki buz oluşum şekilleri ve miktarları, birikme etkinliği ve ısı transferi katsayı sonuçları kanat, kuyruk ve silindir yapılarındaki referans veriler ile büyük oranda uyum göstermektedir. Runback ve çok adımlı çözüm yaklaşımlarıyla fiziksel açıdan daha gerçekçi bir sonuç elde edilmesi amaçlanmıştır. Durma noktasının üst bölgesinde serbest hava akışının damlacıklar üzerine uyguladığı kayma gerilimi nedeniyle damlacıklar komşu kontrol hacmine geçiş yapabilmektedir ve bu durum runback olarak ifade edilmektedir. Özellikle çok uzun buzlanma sürelerinde zamanla oluşan buzun akış alanı üzerindeki etkisinin azımsanmayacak bir seviyede olduğu görülmüş olup, buzlanma parametrelerine göre zaman ve buz kalınlığı artış kriterleri tanımlanıp uygun adım sayısının belirlenmesi yoluna gidilmiştir. Hava araçlarında buzlanma konusunda Türkçe olarak yapılan ilk çalışmalardan biri olması nedeniyle havacılık ile ilgili terim ve tanımlamaların Türkçe'ye çevirisinde Uçak Mühendisleri Terimleri Sözlüğü [17] kaynak olarak kullanılmıştır.

Abstract:
Ice accumulation on aircraft structures is vital safety concern that may cause to a dangerous situation. It is necessary to prevent critical aircraft surfaces such as wings and control surfaces. The icing causes the failure of the pressure and speed measurement devices and consequently make difficulties for flight control. During landing, the icing on the pilot window along with possible failures in the landing gears may cause major catastrophes. Ice particles formed as a result of icing can cause serious mechanical damage to the aircraft when they are detached from the plane surface and collide with the body or aircraft tail or sometimes with internal parts such as compressor blades.

The droplets which cause the aircraft icing can stay in liquid water form  even while the ambient temperature is far beneath solidifying, when they are stuck by the aircraft during the flight. Droplets in the clouds may solidify quickly and structure rime ice on solid wing-circle surfaces or run downstream and solidify some part of incoming droplets which shaping glaze icing type.The sum and rate of icing rely upon various parameters. Of essential significance are the measure of LWC of droplets, size, the temperature of impingement surfaces, the collection efficiency, and the diameter of droplets. Icing risk levels are classified as trace, light, moderate and severe which relies upon the sort of clouds, the kind of aircraft. The appropriation of potential aircarft icing zones is for the most part a component of cloud structure and temperature, which thus differ with level of flight, area and season.

Strati-form and cumuli-form clouds present icing conditions. Ice accumulation may likewise originates from solidifying shower simply close to the cloud base where the droplets are expansive. A few kinds of precipitation cause critical icing conditions while others may show the nearness of critical icing in the region. Solidifying precipitation in front of warm fronts present a severe icing for airplane flying close to the highest point of the virus air mass underneath a profound layer of warm air. This is on the grounds that downpour drops are a lot bigger than standard mists beads and may prompt high fluid water content. Icing may likewise originates from solidifying sprinkle simply close to the cloud base where the droplets are large.


Numerous test have been executed and numerical codes have been developed to explore ice gradual addition on aircraft. By and by, more work is embraced to comprehend the physical part of icing and to configuration better ice assurance frameworks. In the meantime, because of some ongoing icing related accidents and advances in cloud material science instrumentation, numerous exchanges are presently focused on the flow FAA criteria in FAR 25 which depend on research flights attempted 50 years back. The principle objective is the re-assessment of the old information and the impediment of FAA icing envelopes, especially for SLD that surpass the greatest measurement in the FAR 25 criteria. The present report gives a complete review of the best in class in the region related with aircraft in-flight icing including the circumstances and logical results just as icing forecast models. It likewise gives a reference handbook which can be utilized by specialists and analysts as a guide in the improvement of hypothetical and exploratory models to simulate and prevent hazardous icing regions.


Ice accumulation is characterized as that condition where water droplets solidify on aircraft, motors, propellers or rotors and structure measure of ice which bother the free air flow. As indicated by the Federal Aviation Administration (FAA) icing is characterized as the condition where we have obvious stuck and temperature of the surface underneath solidifying. The icing on aircraft surfaces, for example, wings, tail, elevator, rudder and motor admissions,occurs when the aircraft passes in a cloud group where the temperature is at, or underneath the point of solidification and hits water droplets on these critical components. The rate of heat transfer from the flying aircraft surfaces is with the end goal that a few or the majority of the water droplets are solidified before they can keep running back along the surface. The droplets solidify upon effect by shaping  new surface geometry of rime ice accumulation, if all the impinging water freeze, or glaze ice accumulation if just a small amount of the water droplets solidify while the rest of back along the surface or along existing ice and stop downstream. The sum and the state of ice gathered depend for the most part on LWC, temperature, velocity, droplet diameter.


To see how icing in flight happens, it is essentially to comprehend the component and the organization of cloud, and the attributes of water vapor. Indeed, in spite of the fact that water vapor is discovered just in the lower dimensions of the climate it is considered as the most imperative gas from the angle of climate since it can change into water droplets (fluid) or ice precious stones (strong) under various air state of temperature and weight and turns into a genuine perils for air vehicles. There exists two kinds of clouds where air vehicle icing can happen: (i) strati-form clouds and (ii) cumuli-form clouds. Strati-form clouds structure in flat layers. Icing conditions are less serious than in cumuli-form mists, be that as it may, presentation to the icing can be delayed because of the extraordinary flat broaden. Icing in the strati-form clouds is light to direct with most extreme in the upper layer. The most much of the time icing in strati-form clouds is rime ice. In cumuli-form clouds air contains an extraordinary amounts of water droplets. The vertical disturbance may bolster super-cooled extensive droplets which may frame a glaze ice on the uncovered surface of an aircraft and become an important risk in a brief time interval.


There exists essentially two distinct kinds of ice accumulation which structure on aircraft while passing through clouds, containing super-cooled droplets. Icing is categorized to as rime and glaze ice. Rime type icing can be defined as dry (no liquid water include), white color ice store which for the most part happens at low free flow velocity, low temperature and low LWC. It is described by the prompt solidifying of the approaching super-cooled water droplets when they hit the outside of the body catching in the air flow. As a result, the state of the surface is modified creating execution penalties because of the decreasing in the aerodynamic performance and to the additional weight which presents an unbalance of the air vehicle segments at the flight conditions. Glaze icing is a wet development ice framed at a temperature around 0ºC and a high LWC. It has an glaze appearance and a thickness closer to that of the cloud water demonstrating the wet idea of this icing type. It happens when just a small amount of the water droplets solidifies upon effect while the rest of keep running back along the surface or along and solidify downstream.


The sum and rate of icing rely upon various meteorological and aerodynamic conditions, for example, fluid water content, temperature, droplet distance across, and collection efficiency. Liquid water content (LWC) is characterized as the sum or all out mass of water contained in a given unit volume of cloud. Units of LWC are typically given as grams of water per cubic meter of air. From the diverse parameters influencing icing on aircraft, the fluid water content is considered as the most essential. At the point when LWC is high, at that point there is an extraordinary capability of icing. The variety of LWC depends for the most part on the temperature. LWC diminishes with precipitation since accessible water droplets are cleared out, or when there is dissipation as on account of dry air blending with cloud. The fluid water content of cloud as a rule increments with tallness for temperatures not far beneath softening, yet diminishes when temperatures are well underneath melting because of the high measure of ice precious stones. The temperature has an incredible consequences for the portion of water that solidifies on effect, subsequently it will affect the sort of ice which will gather. At the point when surface temperature isn't a long way from solidifying and droplets are extensive, at that point just a little part of the affecting droplets will freeze, while the rest of stop downstream. Ice shapes will likewise change contingent upon the time the aircraft is presented to icing. Droplets present in the environment have diverse widths. In icing simulations, it is used for the most part utilize the medium volume droplet measurement (MVD) defined as the distance across separating the all out water volume into equal parts, where a large portion of the volume is in bigger droplets and a large portion of the volume in littler droplets. Substantial droplets are bound to sway on the airfoil while little droplets are passed. Along these lines, ice may shaped past ice security frameworks. Since large droplets have higher inertial power and negligible terminal velocity contrasted with little droplets, they encroach straightforwardly on the airfoil while the little droplets are diverted. The droplet measure impacts the rate of icing through the expansion of collection efficiency and the difference in the upper and lower impingement limits which move further downstream. Collection efficiency is characterized as the proportion of the mass of droplets impinging on the solid surface. The icing rate and freezing fraction depend to a much degree upon the accretion efficiency of the air vehicle surface. This parameter is critical since it is expected to quantify the rate of super-cooled water droplet impingement, in $kg/hour/meter$ of range, for an airfoil geometry and cylinder. Velocity affects the ice shapes and at the point for the condition, higher velocity prevent the water droplets get a sufficient opportunity to miss from the solid surface. As an outcome, higher collection efficiency will be created. The ice forming on the solid surface will be more noteworthy than the situation where the velocity is low. Also, the speed affects the icing type. High speed generally leans on more forming glaze icing than rime icing.


The primary goal of ice recreation is the estimation of the impingement of the droplets on the aircraft component profiles which decides the droplet impingement districts just as the mass of fluid on the body surface and, all the more especially, the digression or farthest point directions used to decide get dispersion or the worldwide and nearby accumulation effectiveness. There are four principle parts in an icing recreation, I) flow field estimation around profile , ii) water droplet directions in flow field, iii) thermodynamic examination, and iv) ice accumulation model. The computational strategy is an multi step procedure with a period venturing methodology where progressive slight ice layers are accumulated superficially and pursued by flow field and droplet impingement recalculations. The flow field estimation gives the velocity field at the around airfoil surfaces just as anytime in the field far from the surface. The droplet directions are dictated by explaining the condition of movement to acquire the whole way for every droplet moving in the flow field and hitting or passing the solid surface. When the direction ways are referred to, the droplet impingement confines just as the worldwide and neighborhood gathering efficiencies can be determined utilizing an effective output methodology of the frontal surface of the solid surface profile. The computation of the water transition impinging on passing on each surface panel the solid surface can be performed, at that point the ice growth is determined and the geometry is updated characterizing the ice shape out of the between time intervals. The system is then performed at the next time to modify the nodes of panel.


To calculate the velocity field around the profiles, the flow-field calculation with potential theory is used for the goal that the droplet trajectory equations can be solved. In some simulation computer programs, utilized Navier-Stokes estimations to get flow-field calculations, more accurate than potential flow theory but also slower. This is because of the utilization of exact models to comprehend vitality balance and to the restricted comprehension of surface harshness with ice. As a result, it is progressively helpful to utilize a basic model, for example, Hess Smith panel method, to ascertain the flow-field velocity and afterward perform droplet directions. On account of multi-element airfoils, an augmentation of the Hess and Smith panel method to single element has been created.



The droplets are released far away from the airfoil or cylinder and path way of them is calculated with equations of motion in two dimension until impact on the solid surface or achieving a specific  location. In two dimensional Cartesian coordinates, only drag, buoyancy and gravitational forces acts on the droplet passing in flow field. At any integration calculation term, the local velocity needed to solve the droplet equation of motion is obtained from the flow field solution while the integration is continued following droplets until they contact with the solid obstacle or pass downstream of it. The droplet trajectory equation represents a second order differential equation which can be solved using classical difference methods. The drag force is determined using steady-state drag coefficient for a perfect sphere which is a function of Reynolds number. In the Lagrangian method, the trajectory of every droplet is figured dependent on a force balance. A water droplet is viewed as perfect circle that don't influence the flow field however except for aerodynamic drag.Besides, the gravity force can be overlooked for little droplet breadths. The water droplets are "discharged" at an adequately far off position from the body with the goal that the wind current isn't influenced. The direction conditions are comprehended until it blocks the surface. As far as possible are figured by an iterative procedure. For as far as possible, a direction hitting the body and the following one above which does not hit the surface are picked. A direction lying somewhere between these two is processed. On the off chance that it misses the body, it is considered as the new direction which hits the surface. On the off chance that it encroaches the body it is the new hitting direction. This system is rehashed until the hole of the underlying position of the two droplets is littler then a predetermined value. In this study, it is accepted that the water droplets don't influence the flow field and the water unknowns are calculated freely. Lagrangian methods are increasingly proper for basic two-dimensional geometries, since it is computationally practical for such icing problems on aircraft.


The subsequent stage is to play out a thermodynamic investigation on the outside of the surface. The model depends on mass and energy conservation law of thermodynamics in a control volume superficially. In the view of the energy balance and the mass transition, the part of the solidifying water droplets on each control volume can be resolved. The methodology is rehashed for the adjoining control volumes and proceeded with the whole surface. The conservation of mass can be considered the mass flow rate of the incoming and out-coming water flow in the control volume. The energy equalization can be considered the convective heat losses, the friction heat , the enthalpy related with the incoming and out-coming mass at the control volume, the enthalpy related with dissipation or runback to next control volumes, and lastly the interior energy, determined in connection to a given reference state contingent upon the kind of surface included. The model created depends on studied by Extended Messinger Model in two dimension.


The current examination intends to build up a computational computer program for icing recreations on single element wing, tail profiles, control surfaces and cylinders. Fortran language was used to be written the computer program simulation. In the first part of the computer program, flow-field calculation with Hess Smith panel method is executed. Then, droplet trajectory and collection efficiency according to Lagrangian approach is derived in the second part by using flow field velocity calculation outputs of the first module. At the thermodynamic calculation, heat transfer coefficient estimations are examined. Surface tangential velocity distribution calculated in the first module is integral boundary layer calculations for the laminar and turbulence flow regimes. Ice accumulation demonstrates with one dimensional and two dimensional dimensional Extended Messinger Model. Icing examinations on single element wing/tail and cylinders geometries are performed with the created computer program. The outcomes are approved with exploratory and numerical information accessible in writing. Flow field, ice shape expectations, droplet collection efficiency and heat transfer coefficient results got in the present examination are generally in acceptable error tolerance concurrence with reference results for airfoil and cylinder cases. Be that as it may, the ice shape results for glaze icing conditions, current methodologies and suppositions include some shortcoming when ice shape and impingement locations are considered. So as to get increasingly exact ice shapes framed while glaze icing conditions, it is recommended the exactness of the thermodynamic examination by including micro-physical impact, droplet geometry and droplet impact angle.