THERMAL ANALYSIS OF SECOND STAGE GAS TURBINE ROTOR BLADE
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1 Polymers Research Journal ISSN: Volume 6, Number 01 Nova Science Publishers, Inc. THERMAL ANALYSIS OF SECOND STAGE GAS TURBINE ROTOR BLADE E. Poursaeidi, M. Mohammadi and S. S. Khamesi University of Zanjan, Iran ABSTRACT One of the most important parts of the axial turbines is the blades of rotor, which are under bending, torsion and thermal stresses due to high combustion product temperature. In fact the combustion products have high temperature, since they are produced in the combustion chamber in gas turbines. Rotating blades of turbine will rotate with high rotational speed due to kinetic energy of the flow. In this paper, the process of designing gas turbine blades base on thermodynamics relations is reviewed. Moreover, this designing is developed by mathematical and thermo dynamical governing equations. The thermo dynamical analysis results are shown in temperature, pressure and velocity distribution graphs. In this research, temperature distribution of a second stage typical gas turbine rotor blade, under real conditions is computed by using computational fluid dynamics methods. Also the decreasing of temperature and increasing of heat transfer are reviewed as a result of blades height decrease. Keywords: thermal analysis of turbine, rotor blade, computational fluid dynamics, turbulence model, temperature distribution INTRODUCTION A perfect CFD analysis of a typical turbine based on its real conditions can develop the process of designing gas turbines. Time of computation and amount of memory usage, are different in various kind of CFD methods and the precise result of various methods is another challenge for finding the correct answer. Some parameters such as: complex geometry, unsteady flow, relative motion, and turbulence, makes the analysis more complicated. moreover, this complexity will be increased in gas turbines due to high temperature of inlet flow and high rotational velocity of rotor blades. On the other hand, according to the high rotational speed, these blades are imposed to various types of forces such as: centrifugal force and so they are more vulnerable. So in this paper the CFD analysis is done for the rotating epsaeidi@znu.ac.ir
2 168 E. Poursaeidi, M. Mohammadi and S. S. Khamesi blades. Also the behavior of the fluid flow on the second stage of rotor blades is studied which is modeled under real conditions of a typical industrial gas turbine. TURBINE THERMODYNAMIC ANALYSIS At first, it is necessary to consider thermodynamic analysis for computing the stage number, number of rotors on each stage, inlet and outlet velocity, inlet and outlet angle of flow on blades, temperature profiles and pressure in inlet and outlet of blades. The result of this analysis is a key solution for finding considered profiles and studying the turbine elements accurately. The base of energy conversion in gas flow is due to converting the potential energy to the kinetic energy. This process will be done by forcing gas flow through stator and rotor blades. The kinetic energy of the flow will be decreased in rotating blades and will be recovered in stators. So it is obvious that in this process the density of flow will be decreased and if the axial velocity of the flow kept constant, then the height of the blade will be increased. For describing the flow condition among turbine stages, the below assumptions are considered: 1. Flow conditions in mean radius are taken into consideration except the implied cases.. The ratio of the blade height to the mean radius is low therefore we can use the theory of two dimensions flow.. Fluid radial velocity along the turbine is zero. 4. The entry fluid into the turbine has been taken account as ideal gas. Table 1. Entry Parameters of a 50mw Power Satation Parameters Inlet Static Pressure (Pascal) Inlet Temperature ( C) Flow Rate (kg/s) Rotating Velocity (rpm) Amount VELOCITY TRIANGLE ANALYSIS Velocity diagram for one stage of turbine is according to figure 1. According to figure 1 the velocities are: U: blade linear velocity C, C : fluid absolute velocities V, V : fluid relative velocities α, α : entry angle into the nozzle and out of the nozzle β, β : entry angle to the moving blade and out of it.
3 Thermal Analysis of Second Stage Gas Turbine Rotor Blade 169 Figure 1. Velocity Tiangle in Fisrt Stage of the Turbine. Before velocity analysis, it is necessary to introduce three dimensionless parameters for turbine designing: 1. Blade force coefficient or the temperature difference coefficient which indicates the work capacity of each stage. C T p U os C U a (tan tan ) (1) where the terms of Eq. (1) are as follows: ΔT os : temperature difference in each stage C p : specific heat of fluid on constant pressure C a : velocity. Reaction degree: Ca (tan tan ) U (). Flow coefficient C a U ()
4 170 E. Poursaeidi, M. Mohammadi and S. S. Khamesi COMPUTATION OF ENTRY AND EXIT ANGLES AND THE FLUID VELOCITY The following amounts were taken into account pressure ratio p ΔT os is computed from Eq. (5) T os T P 01 1 P 01 1 P 0 1 (4) By knowing ΔT os, blade force coefficient can be computed from equation (1). Now by finding ψ amount, Λ and inlet and outlet angles of flow can be computed from the following relations[1,]: tan tan 1 1 tan (0.5 ) 1 tan (0.5 ) tan tan 1 (5) (6) (7) (8) By knowing α and by using equation (8), the axial velocity of the flow can be calculated. Ca C cosα (9) For calculating the other velocities: Where C a is the flow axial velocity and is obtained from Eq. (10). C a U (10) Which it has been taken into account from reference [1]
5 Thermal Analysis of Second Stage Gas Turbine Rotor Blade 171 C V V Ca cos Ca cos Ca cos (11) (1) (1) Temperature Distribution The net work of nozzle is zero, so according to the first law of thermodynamic it will be proved that: 0 T 0 T T 17K h 01 0 Thus, T' is obtained from Eq[]. (14) T 0 T N C c p (14) Pressure Distribution Pressure distribution in each section is obtained from Eq(4) to (15). [5] P P 0i i1 T ( T 0i i1 ) 1 ( ) (15) Blades Area Computing For achieving to blades area, after computing temperature and pressure distribution, the flow density, is obtained from Eq. (16). P RT (16) Then the intended areas which are shown in Figure will be obtained. (According to Eq. (17)) A m C a (17)
6 17 E. Poursaeidi, M. Mohammadi and S. S. Khamesi Figure. Exhibition of Sections under Review. Blades Height Computation Blade mean radius has been computed from Eq. (18) and then by using Eq. (19), blade height, h, was computed. U h m Nr m AN U m (18) (19) GEOMETRY AND MESH For exact and real simulation of the gas turbine moving blade at the first step, the general geometry of the design was characterized by using the industrial plans and gas turbine moving blade. For simulation and perform the finite volume computations a proper mesh is required, that Gambit. software was used for this purpose. The intended mesh according to the following picture was produced. In this software the mesh quality was formulated very carefully that in view of accuracy and the time of performing computations it is optimum perfectly. The produced mesh for finite volume analysis is recalled in Fluent 6. software. FLOW SIMULATION The rotating blade has been simulated by using single reference frame model. For this modeling relative velocity terms are included in the governing equations. On the other hand this model has a problem which is due to high radial pressure gradient.
7 Thermal Analysis of Second Stage Gas Turbine Rotor Blade 17 Because of high rotation velocities, this pressure gradient will be produced and forces the fluid to flow across the axis and radius. Consequently this phenomenon makes the solving process unstable. Figure. Prepared mesh in Gambit.. Relative velocity v v r u r (0) Mass continuity d v dt e 0 (1) Momentum continuity d ( vr ).( vrv dt r ) ( v r r ) p () TURBULENCE MODEL Turbulence flow features are the velocity variation with time and three dimensional velocity fluctuations. These fluctuations affect other terms of the momentum and energy equations. Choosing the turbulence model for simulating flow depends on problem specifications, accuracy and time of solving. In this simulation three kinds of k-ε models are reviewed. These are: Standard RNG Realizable
8 174 E. Poursaeidi, M. Mohammadi and S. S. Khamesi The first turbulence model is k-ε Standard, which uses two other equations for k as turbulence speed and the other for ε as characteristic length. This model was purposed by Launder and Spalding [6], which it s results, has fair agreement with experimental results. After finding advantages and disadvantages of this model, RNG and Realizable models were developed. BEHAVIOR OF THE FLOW ON THE WALL In the boundary regions beside the wall, due to existence of the pressure and velocity gradients in the fluid, turbulence modeling needs a specific accuracy. The regions on the wall divide into three following parts [7]: 1. Viscous under layer which has a perfectly laminar flow.. Middle layer which the viscosity and turbulence influences on it is very important.. The outer layer which has the perfectly turbulence flow. In this part below models are used for modeling the wall effects: 1. Standard wall function. Non equilibrium wall function. Enhanced wall treatment The first model has great accuracy in high Reynolds numbers. The second model can include pressure gradient and the last model is used for simulating the middle and outer layer by using ε and turbulent viscosity. This model needs very fine mesh. Due to simulation the two middle and outer layers, enhance wall function model is used, for reviewing turbulence on the wall. BOUNDARY CONDITIONS The boundary conditions which are essential for defining the variables in this model are shown in figure.
9 Thermal Analysis of Second Stage Gas Turbine Rotor Blade 175 CONVERGENCE During solving geometries with rotary reference frame and rotary flows with high velocities due to coupling momentum equations which produce great rotary terms, result converging is delayed. The high rotary velocities cause to produce high radial pressure gradient which make the flow move along axial and radial directions. Coupling these momentum equations causes solve instability which needs a specific techniques to converge. In this paper for increasing the speed of solving, relative velocities are included in the momentum equation. The under relaxation factors are about 0.6 for momentum and about 0.7 for turbulence viscosity. Figure 5. Flow Field Equations Convergency Diagram. RESULTS AND COMPARISON The Height Decrease Effect on the Temperature Distribution The obtained temperature distribution for two blades with the characteristics of the Table is according to Figures and 4. Table. Analyzed blade height Optimized moving blade height [m] 0.1 Real moving blade height [m] 0.
10 176 E. Poursaeidi, M. Mohammadi and S. S. Khamesi Figure. Temperature contour for blade with 0.1 m height. Table. Inlet and outlet static and total temperature of 0.1 and 0.0 m blades Blade height Inlet static Outlet static Inlet total Outlet tota [m] temperature[ C] temperature[ C] temperature[ C] temperature[ C] Table 4. Average temperature of 0.1 and 0.0 m blades Blade height [m] Average temperature of blades area [ C] Average temperature of control volume [ C] Optimized blade (0.1 m) Real blade (0.0 m)
11 Thermal Analysis of Second Stage Gas Turbine Rotor Blade 177 Figure 4. Temperature contour for blade with 0.0 m height. The Height Decrease Effect on the Heat Transfer Rate Table 5. Heat transfer rate from 0.1 and 0.0 m blades Blade height [m] Inlet heat transfer rate[w] Outlet heat transfer rate[w] Total heat transfer rate[w]
12 178 E. Poursaeidi, M. Mohammadi and S. S. Khamesi DISCUSSION AND CONCLUSION According to tables, 4 and 5 the optimized blade has more heat transfer tare and its loss of temperature is more than the real blade. The computations show that reducing the height from 0. m to 0.1 m makes more temperature loss and in fact more heat transfer rate. These results are shown in tables 6 and 7. Table 6. Heat transfer rate of blades Blade height [m] Heat transfer rate[w] Outlet heat transfer rate[w] Optimized blade (0.1 m) Real blade (0.0m) Table 7. Temperature loss percent Percent of outlet temperature loss Percent of blades area average temperature loss Percent of control volume average temperature loss 1.54% 0.5% 0.57% REFERENCES [1] H. Cohen, G. Rogers, H. Saravanamutto, Gas turbine theory. Britain, Longman Group Limited, [] P. B. Meherwan, Gas turbine engineering handbook, USA: Elsevier, 001. [] J.P. Holman, Thermodynamics, Mc Graw-Hill [4] J. D. Anderson, Modern compressible flow, USA: McGraw-Hill Book Company. [5] H. Abbott, A. E.Von Doenhoff, Theory of Wing Sections, Dover Publications. Inc, New York, [6] S. Khamesi, M. Mohammadi, E. Poursaeidi, Design a Typical Gas Turbine based on Thermodynamic Relations and CFD Analysis of Its Rotor Blade, ASME-JSME-KSME Joint Fluids Engineering Conference 011 (AJK011-FED). July 4-9, 011. Hamamatsu, Japan. [7] B. R. Munson, D. F. Young, T. H. Okiishi, W. W. Huebsch, Fundamentals of Fluid Mechanics, 6 th ed, Jhon Wiley and Sons, 010.
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