Gaz türbin kanadı üzerinde iki boyutlu sıcaklık dağılımının çıkartılması
Two dimensional temperature distribution on a gas turbine blade
Yazar: İBRAHİM KOÇ
Danışman: DOÇ. DR. İ. CEM PARMAKSIZOĞLU
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü
Derece: Yüksek Lisans, 1994
Konu: Enerji = Energy ; Makine Mühendisliği = Mechanical Engineering
Dizin: Enerji = Energy ; Gaz türbini = Gas turbine ; Isı dağılımı = Heat distribution

Özet:
ÖZET Gaz türbin veriminin arttırılması, türbin giriş sıcaklığının, kanat malzemesinin izin verdiği oranda yükseltilmesine bağlıdır. 1100-1200°C mertebesindeki bu sıcaklıklara çıkabilmesi ancak malzemenin etkin bir biçimde soğutulması ile gerçekleştirilmektedir. Çalışmada, türbin kanat soğutmasında kullanılan soğutma metotları, kanat malzemesi hakkında bilgiler özetlendikten sonra bir gaz türbini kanat kesiti üzerindeki sıcaklık dağılımının sonlu elemanlar yaklaşık çözüm metoduyla üçgen eleman kullanılarak incelenmiştir. Hazırlanan bilgisayar programı FORTRAN 77 diliyle hazırlanıp, akış şeması EK-A da, program EK-B dedir. VI

Abstract:
SUMMARY TWO DIMENSIONAL TEMPERATURE DISTRIBUTION ON A GAS TURBINE BLADE Our understanding of turbine heat transfer and aerodynamics has increased considerably over the past 50 year, driven by the need for increased performance and life and aided by the evolution of new computational and experimental techniques. The actual output at the generator terminals will be much less than this. A gas turbine plant consists of a tubo-compressor,combustion chamber (or a heat exchanger) and turbine. When the compressor develops enough pressure to support combustion of the fuel in the combustion chamber, the hot gases can themselves drive the turbine and the plant is the difference between the turbine work and the copressor work. If the gas turbine plant is used as an aircraft engine the net output at the turbine shaft 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 overall thermal efficiency of a gas turbine plant is a function of many paremeters namely: specific heat ratio of the hot gas, pressure ratio of the plant the component efficiencies and the ratio of maximum and minimum temperatures. Among these the most effective and influential one is the last parameter^he ratio of maximum and minimum temperatures. At present the component efficiencies are in excess of 85%, thus they can be considered 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 minimum 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 temperature which is the maximum temperature point of system. The main objective of the gas turbine research is the development of enjines with more power, less fuel corruption and also less weight Although substantial improvements are possible by increasing the aerodynamic efficiency of the different egine components, the largest benifits are obtained from higher turbine entry temperatures(TET). A 35/1 pressure ratio and a 1800 K TET are typical values observed in high performance jet enjines. However, material propertiesmost often impose a limit to these thermodynamic inlet condition; internal and/or external cooling systems had to be developed in order to allow further increase of the TET, without affecting dramatically the blade life characteristics. The turbine inlet temperature is limited by current materials. When the blade temperature rises above 1000 C material properties such as creep strength, fatique and oxidation resistace fall rapidly. A composite material of tungsten reinforced superalloy may endure a temperature of 1100 C being superior to ordinary superalloys which may withstand up to 1000 C. From metarials point of view, a 20 C increase in metal temperature may halve the life of a blade, over certain specified temperature limit. Improvements in metarials have allowed the maximum turbine inlet temprature to increase slowly with time, but egine designers have had to seek ways of increasing the turbine inlet temperature at rate faster than materials will allow. One solution has been the use of turbine cooling, which has allowed the turbine designer to increase the türbin inlet temperature while maintaining a costant blade temperature. In order to employ high gas temperatures in gas turbine stages it is necessary to cool the casing, nozzles, rotor blades and discs. On account of high rotational speeds and the associated stresses, cooling of the rotor blades is more critical. Cooling of these components can be achieved either by air or liquid cooling. Liquid or water cooling, if possible, appears to be more attractive on account of the higher specific heat and possibility of evaporative cooling. However, the problems of leakage, corrosion, scale formation and choking militate against this method. The four turbine blade cooling methods are convection cooling, impingement cooling, film cooling and transpiration cooling. Early cooling methods were rudimentary whereby air was passed through hollow blades, this was subsequenty refined to groups of small radial passages with cooling air flowing from root to tip. The nozzle guide vanes from these engines generally incorporated fabricated* metal insert which cooled the component with a combination of impimgement and convection flows. Over the pass decade significant improvements accrued from the introduction of film cooling together with complex internal cooling passages on both blades and vanes. Internal convection cooling of gas turbine blades through forced convection by circulating compressor extraction air inside, the blade is one of the most commonly used methods. The air flows in; a holow interior or cooling passages inside the blade. VlllMost internally cooled rotor blades have their cooling air supplied into massages starting within the blade root and deV&loping in the spanwise direction towards the blade tip. The air is usually discharged through the tip which often carries a shroud and a sealing system or through a film cooling configuration across the external surfaces of the blade. Convective cooling is used where the avarage cooling effectiveness levels required are less than about 0.5. This limitation exists for two reasons; (1) the air supply pressure is limited and much higher effectiveness would be possible onl with higher supply pressure; (2) with high effectiveness levels and convective cooling, the temperature gradients tend to become very large thus aggravate thermal stress problems. The airfoil external heat transfer coefficient 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 of the heat transfer coefficient are very high,the impingement cooling method seems to be powerful. The coolant used in inpingement then travels through the inner skin of the blade and is discharged from the trailing edge. Impingement cooling is a very effective method in local areas and is easily adapted to stator (nozzle) blades. This method may be used in rotor blades if sufficient space is available to include the required hardware inside the blade.This method is usually employe at the leading edge of the blade, but it may be used in other areas if desired. Another convective technique commonly used to obtain high heat transfer coefficients is to place fins normal to the coolant flow paths. By this way moderately high heat transfer rates can be obtained. With the levels of cooling supply pressure generaly available in turbines, it becomes very difficult to convectively cool airfoils at average cooling effectiveness values greater than about 0.5. When the turbine gas temperatures, coollant temperatures, and allowable metal temperatures require a higher effectiveness level, film cooling is utilized. Film cooling involves the injection of a secondary fluid (air) 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. IXFilm 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 are required in the blade because cooling effect of the film is quicly dissipated by downstream of the film air with mainstream gases. Transpiration 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 of materials with uniform porosity and the possibility of local clogging due to harsh environment of a gas turbine engine, limit the extensive use of such a cooling scheme. 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 differential equations with simple boundary conditions are the result. When analytic tecniques of solving differrential equations fail, finite elements or some other numerical method must be used to obtained a solution. Generaly the complexity of the finite element method for a particular problem will be proportional to the complexity of the differential equation for that particular problem. A simple heat conduction problem resulting in a second order differential 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 differential 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. Spesific points within the elements, such as the corners of 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 polynominals are used as interpolation functions because they are easy to differentiate and intagrate.Each element makes a contribution to the overall region that is a function of element geometry, material properties, number of nodal points degree of interpolation function, and other variables. So the element properties must be assambled to form a set of algebraic equations for the nodal values of the physical variablesln the case of linear systems described by linear differential equations, me resulting algebraic equations will be linear in form and can be assambled using matrix techniques. Since the global are linear many standart techniques are available to solve them. Some of these are direct such as the Gauss-Elimination method, while others are iterative. After this step, the accuracy of the numerical solution of differential equations must be verified. The exact solution to the problem being analyzed usually is not known. Therefore the accuracy of the approximate solution obtained through the finite element method may not be known. In other words, it is not known beforehand 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 deterniining the gas side temperature distribution the temperature range in which the blade materials can withstand has been taken into count. Then the datas have been put into the computer program which is based on the approximate finite element metedology and the nodal values have been found by the virtue of the running program. XI