Gaz türbin kanadı üzerinde iki boyutlu sıcaklık dağılımının çıkartılması
Two dimensional temperature distribution on gas turbine blade
Yazar: MURAT ÇAKAN
Danışman: PROF. DR. ALPİN K. DAĞSÖZ
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü
Derece: Yüksek Lisans, 1992
Konu: Makine Mühendisliği = Mechanical Engineering
Dizin: Gaz türbini = Gas turbine ; Isı dağılımı = Heat distribution ; Sonlu elemanlar yöntemi = Finite element method ; Türbin = Turbine

Özet:
Gaz türbin veriminin arttırılması, türbin giriş sıcaklığının, kanat malzemesinin izin verdiği oranda yükseltilebilmesine bağlıdır. 1100-1200°C mertebesindeki bu sıcaklıklara cıkılabilmesi ancak malzemenin etkin bir biçimde soğutulması ile gerçekleştiri lebiImektedir. Bu çalışmada, türbin kanat soğutmasında kullanılan metotlar özetlendikten sonra ele alınan bir gaz türbin kanat kesidi üzerindeki sıcaklık dağılımı sonlu elemanlar yaklaşık çözüm yöntemiyle incelenmiştir. Bu yöntem ile bulunan sıcaklık dağılımı daha sonra aynı geometri ve soğutma konfigürasyonuna sahip bir kanat için "ANSYS" sonlu elemanlar programı ile bulunan çözüm ile karşılaştırılmış ve doğrulaması yapılmıştır. Hazırlanan algoritma bir FORTRAN 77 programı olarak EK-A'de sunulmuştur.

Abstract:
A gas turbine plant consists of a turbo-compressor, combustion chamber Cor a heat exchanger) and turbine. The plant is started by rotating the compressor-turbine assembly by a starting motor or any other device» When the compressor develops enough pressure to support combustion o-F the -Fuel in the combustion chamber, the hot gases can themselves drive the turbine and the plant becomes sel -F- sustaining. The output of the plant is the difference between the turbine work and the compressor work. The actual output at the generator terminals will be much less than this. I-F the gas turbine plant is used as an aircra-Ft engine the net output at the turbine sha-Ft is used to drive a propeller in a turbo- prop engine, whereas in a turbojet engine the turbine output equals the power- required to drive the compressor. The output o-F such a plant is the energy in the exhaust gases which is used -For jet propulsion. The overall thermal e-F-Ficiency o-F a gas turbine plant is a -Function o-F many parameters namely s spec i -Fie heat ratio o-F the hot gas, pressure ratio o-F the plant, the component e-F-Ficiencies and the ratio o-F maximum and minimum temperatures. Among these the most effective and in-Fluential one is the last parameter; the ratio oF maximum and minimum temperatures. At present the component e-F-Ficiencies are in excess of 85%, thus they can be considered -Fixed. Also, the speci-Fic heat ratio o-F the hot gas is -Fixed -For a certain -Fluid. Increasing the pressure ratio may increase the overall thermal efficiency but with a heavier and cumbersome plant in hand. Especially in aeronautics, this alternative is not taken into account since the aim is to increase the thrust output from a given engine, to reduce its weight and/or decrease the fuel consumption for a specified output. For aircrafts, the minium temperature of the system is the ambient temperature. For this reason, it is obvious that the overall thermal efficiency of a gas turbine plant is dependent on the turbine inlet temperatue which is the maximum temperature point of the system. IXThe turbine inlet temperature is limited by current materials. When the blade temperature rises above 1000 C material properties such as creep strength, -fatigue and oxidation resistance -Fall rapidly. A composite material o-F tungsten rein-forced superalloy may endure a temperature of 1100 C being superior to ordinary superalloys which may withstand up to 1000 C. From materials point o-f view, a 20 C increase in metal temperature may halve the li-fe o-f a blade, over certain speci-fied temperature limit. Improvements in materials have allowed the maximum turbine inlet temperature to increase slowly with time, but engine designers have had to seek ways o-f increasing the turbine inlet temperature at a rate -faster than materials will allow. One solution has been the use o-f turbine cooling, which has allowed the turbine designer to increase the turbine inlet temperature while maintaining a constant blade (material) temperature. When considering turbine cooling, the -fluid to be used as a coolant has to be selected -first. Air is the most logical choice as a coolant, since it is readily available. It can be extracted (bled) -from the compressor, ducted to the turbine blade (stator or rotor) and used as a coolant. The -four turbine blade cooling methods are convection cooling, impingement cooling,.film cooling and transpiration cooling. Internal convection cooling o-f gas turbine blades through -forced convection by circulating compressor extraction air inside the blade is one o-f the most commonly used methods. The air -flows in a hollow interior or cooling passages inside the blade. Most internally cooled rotor blades have their cooling air supplied into passages starting within the blade root and developing in the spanwise direction towards the blade tip. The air is usually discharged through the tip which o-ften carries a shroud and a sealing system or through a -film cooling con-figuration across the external surfaces o-f the blade. Convective cooling is used where the avarage cooling e-F-fectiveness levels required Bre less than about 0.5. This limitation exists -for two reasons: (1) the air supply pressure is limited and much higher e-f-fectiveness would be possible only with higher supply pressures? (2) with high e-f-fectiveness levels and convective cooling, the temperature gradients tend to become very large thus aggravate thermal stress problems. The air-foil external heat transfer coe-f-f icient distribution across the surface of the blade must be counterbalanced with a comparable heat transfer coefficient distribution on the inside of the airfoil.Especially at the leading edge where the stagnation point values o-F the heat transfer coefficient are very high, the impingement cooling method seems to be powerful. The coolant used in impingement then travels through the inner skin of the blade and is discharged from the trailing edge. Impingement cooling is a very e-F-Fective method in local areas and is easily adapted to stator * nozzle) blades. This method may be used in rotor blades i-F sufficient space is available to include the required hardware inside the blade. This method is usually employed at the leading edge o-F the blade, but it may be used in other areas if desired. Another convective technique commonly used to obtain high heat transfer coe-F-Ficients is to place fins normal to the coolant flow path. By this way moderately high heat transfer rates can be obtained. With the levels of cooling supply pressures generaly available in turbines, it becomes very difficult to convectively cool airfoils at avarage cooling effectiveness values greater than about 0.5. When the turbine gas temperature, coolant temperature, and allowable metal temperature require a higher effectiveness level, film cooling is utilised. Film cooling involves the injection of a secondary fluid into the boundary layer of the primary fluid (hot gas). This is an effective way to protect the surface from the hot gases by directing the cooling air into the boundary layer to provide a protective, cool film along the surface. The injection of the coolant air into the boundary layer causes turbine losses, which tend to reduce some of the advantages of using higher turbine inlet temperatures. Also, if too much air is injected into the boundary layer or the velocity is too high, the cooling air may penetrate the boundary layer defeating the purpose of using film cooling. If the holes are placed too close together, stress concentrations, which could be detrimental to engine performance and reliability, may occur. Film cooling is more effective than normal convection cooling or impingement cooling. The cooling air absorbs energy as it passes inside the blade and through the holes, then further reduces the metal (blade) temperature by reducing the amount of energy transferred from the hot gases to the blade. It should be noted that a large number of small holes mre required in the blade because cooling effect of the film is quickly dissipated by downstream mİMİng of the film air with mainstream gases xi rTranspiration cooling is considered to be the ideal cooling method. In this method, coolant is introduced through a porous wall, so that it convectively cools the porous wall to the maximum theoretical limit (metal temperature equals coolant discharge temperature) and also.Film cools it with a well distributed low velocity coolant- However the thermal and mechanical strength of the present day porous materials are quite limited. It is reported that the maximum allowable porous blade material temperature is around 1000 C. The difficulties in the production o-F materials with uniform porosity and the possibility o-F local clogging due to harsh enviroment o-F a gas turbine engine, limit the extensive use o-F such a cooling sc heme. In this study, a two dimensional turbine blade section with internal convective cooling is taken into account and -Finding the temperature distribution due to the internal cooling is aimed at. Unlike this sample, in some cases, simple di-F-Ferential equations with simple boundary conditions are the result. When analytic tecniques o-F solving di-F-Ferential equations -Fail, -Finite elements or some other numerical method must be used to obtain a solution. Seneraly the complexity of the -Finite element method -For a particular problem will be proportional to the complexity o-F the di-F-Ferential equation For that particular problem. A simple heat conduction problem resulting in a second order diF-Ferential equation will result in a correspondingly simple -Finite element analysis. Solving an engineering problem by the Finite element approach -Follows an orderly step- by- step process. Usually the engineering problem can be described by a governing di-F-Ferential equation and associated boundary conditions. The next step is to divide solution region into appropriately shaped elements. For instance, two dimensional areas may be divided up into triangles, rectangles, or other appropriately shaped elements. Within an element the physical variable such as displacement, temperature, pressure, stress, or other variable is to be approximated by a simple -Function, such as a linear polynomial. Specific points within the elements, such as the corners o-F a triangular element, are designated as nodal points. If the temperature at each of the three corners of the triangle is determined and a linear interpolation function for the temperature is used within the element, the temperature over the entire element is known. Usually polynomials are used as interpolation functions because they are easy to differentiate and integrate. Each element makes a contribution to the overall region that is a function of element geometry, material XIIproperties, number of nodal points degree o-F interpolation.Function, and other variables. So the element properties must be assambled to -Form a set o-F algebraic equations for the nodal values of the physical variables. In the case of linear systems described by linear di-F-Ferential equations, the resulting algebraic equations will be linear in -Form and can be assambled using matrij-s techniques. Since the global equations are linear many standard techniques are available to solve them. Some o-F these are direct such as the Sauss- El imi nation method, while others are iterative. After this step, the accuracy solution o-F differential equations must e>;act solution to the problem being not known. Therefore the accuracy solution obtained through the finite not be known. In other words, it is how many nodes are enough to insure an accurate solution. This can be checked by increasing the number of nodes and determining whether the solution at the node points changes or not. The subject of this study has been to find the temperature distribution inside the two dimensional turbine blade section with convective cooling configuration. The gas side heat transfer coefficient distribution along the outer boundary of the blade and the coolant side heat transfer coefficient distribution along the inner boundary of the blade has been taken as constant. Also the blade is assumed to have a constant heat conduction coefficient. While determining the gas side temperature distribution the temperature range in which the blade materials can withstand has been taken into account. Then the datas have been put into the computer- program which is based on the approximate finite element met edo logy and the nodal values have been found by the virtue of the running program. These values then, have been compared to the solutions found by "ANSYS" finite element program and it has been seen that the difference between the solutions have fallen in the same acceptable range. XIII