Simulation of temperature distribution in gas turbine stator blade subjected to different internal coolant gases

in order to simulate the cooling process and the temperature distribution. At first, the air is applied and the results show a good agreement with previous literature then the other coolants compare their results with the air. The results show that the Helium affects the cooling process strongly and it cools the blade to safer limits rather than air by about 50%, but it increases von Mises stress by about 71% in comparison with air. The two other coolants also have a good and effective cooling performance, but they almost show an identical performance.


Introduction
Regarding its merits, gas turbine engines become the most reliable and promising units in many industrial and aviation fields to generate power and thrust force and to compensate loads at peak load situations. The thermal and power output of these engines is still limited by the metallurgical limit of turbine blades. Any higher turbine inlet temperature beyond the fusion point of the blade alloy leads certainly to thermal failure of the unit especially in the presence of a high rotational effect on the rotor.
To avoid such a situation in the operation, a cooling technique is adopted by manufacturers internally to reduce the severe temperatures and to increase the operational hours of the unit as long as it operates at safe limits [1][2][3]. Different cooling methods are proposed like film and internal cooling or both of them depending on the conditions of the application area of the gas turbine engine itself. Among them, is internal cooling, mostly incorporated via cooling passage inside the blade.
Internal cooling configurations also investigate. Burberi et al [12] studied the effect of rotation on the heat imply different geometries and shapes to get better performance and effect [4][5][6][7]. Al Ali and Janajreh [8] performed a theoretical analysis of different configurations of heat transfer via impingement cooling. Moskalenko and Kozhevnikov [9] estimated the gas turbine blade cooling efficiency by simulating two mediums of cooling, i.e., water vapor and air. In their results, they found that water vapor is more efficient than air for the same working pressure and temperature by about 30%. Deepanraj et al. [10] studied by using different models with different holes by using a finite element method to find out the optimum number of holes for good performance. They found that when the number of holes is increased in the blade, the temperature distribution is decreased dramatically. The ribs in the cooling channels play an important role since they increase the turbulence level, which in turn enhances the heat transferred between the inner wall and coolant. Xie et al. [11] studied their effect on different paths at different Reynold numbers. They found an improvement in heat transfer, but the pressure drop should be accounted. Since the blade is mounted on the rotating disc which rotates, usually at a very high rotational speed, the effect of rotation is also has been into account the rotational effect of the gas turbine and thus it has been selected in this paper. Burberi et al. [12] studied the effect of rotation on the heat transfer coefficient especially at the leading edge zone. Their findings indicate an effect at the tip region but it vanishes at the hub region. Optimization of internal cooling is also investigated by researchers in order to find the optimum parameters of the whole process [13][14][15]. Mousavi et al. were also interested in finding optimum cooling. In their works [16,17] they performed a numerical analysis in a three-dimensional model to optimize the hole of cooling serpentines and their distribution along the chord of the gas turbine blade. Their results show a huge reduction in the mass flow rate of the cooling air extracted from the compressor which in turn positively affects the output power and thermal efficiency of the gas turbine engine. Weak attention was directed in previous studies to the type of coolant and its physical properties. Finding an effective coolant has become a challenge as it is influenced by a large number of flow and geometrical parameters. This paper is dedicated to analyzing the gas turbine blade when subjected to different coolants in three case studies to find its effect on the internal cooling and severe temperature distribution.

Mathematical model
The governing equation of the flow field of the flowing air can be expressed as follows:

• Turbulence model
Where ′ ′ ̅̅̅̅̅̅ should be calculated by using a suitable turbulence model.
Because of complex flow phenomena inside the cooling channels of the blade, the type of turbulence model should provide acceptable accuracy in the calculation of heat transfer cooling. Many models had been selected in previous studies to simulate the turbulent heat transfer, among them, the Shear Stress Transport (SST) turbulence model [5] and the Renormalized Group (RNG) k-ε model [18,19] which show a good convergence in their result. A low-Reynolds number (LRN) k-ω turbulence model, with improved heat transfer predictions, is proposed by Bredberg J. in his works [20][21][22][23][24][25][26] which shows better results and convergence, especially as it takes

• Heat transfer in a solid zone
The dominant mechanism of heat transfer in the turbine of the gas turbine engine is the convection heat transfer. Since there's flowing hot gas outside the blades and relatively cold coolant inside the blade flowing through the cooling duct, this model of convective heat transfer seems to be reasonable which is usually defined by: The heat transfer coefficient (α) needs to be calculated accurately and accounted for the well-known dimensionless parameter Nusselt number and the latter itself in the forced convection is a function of Reynold and Prandtl numbers, so The characteristic length of Lc varies for different zones in the gas turbine blade. To obtain precise calculations of the magnitude of heat transfer quantity, the heat transfer coefficient will be calculated in different forms according to zones where a heat transfer occurs.
-Heat transfer in the cooling ducts of the blade

Nomenclature:
Greek -Heat transfer at the top and bottom sides of the blade The same equation above is adopted with a difference in the characteristic length.

Numerical simulation
The numerical simulation is performed using the software package COMSOL Multiphysics® to model the different cases adopted in this study. To isolate the effect of the type of coolant, the operating conditions and other parameters are kept with no change. To obtain good results, a fine mesh was generated near the channel walls and the fluid flow domain to capture the temperature variations because of coolant fluid flow throughout the channels. The blade material was chosen to be a nickel super-alloy Inconel 718, which is being used widely in aerospace-related applications. The physical properties of the coolant are chosen to be a function of temperature as illustrated in Table 2. The values of the constants are taken from the study of [27]. The case geometry is shown in Fig. 1 with the mounting details of the blade. Fig. 2 shows the cooling ducts and the passages where coolant fluid flows inside the gas turbine blade to reduce the severe temperature and hot spot which usually occur on the blade surface because of the hot incoming burned gases from the combustion chamber of a gas turbine engine. The duct geometry does not include any ribs or turbulators.

Mesh generation
In the first step, the blade geometry was built in the Solidworks software. Two camber lines were used to create the side boundaries. Then, this geometry was exported from Solidworks and later imported into COMSOL Multiphysics software to build up the mesh because of its flexibility for creating a mesh. For faster calculations and performance, as we go farther from the blade into the fluid domain, the mesh size becomes larger and larger as shown in Fig. 3

Results verification
The results of the current model of the first common coolant (air) show a good and reliable agreement with the results of many authors who applied their numerical simulation and compared them with the experimental data of many researchers, foremost among them Hylton et al. [28]. Among these cases studies, the case study of [29] had been re-modeled and simulated in the current software program at the same geometry, boundary conditions, and other numerical values, the results were approximately the same in terms of temperature distribution and heat transfer as shown in Fig. 4. Based on this agreement, the other cases are judged to be accepted.

Results and discussion
The main focus in the results section of the simulation process is dedicated to thermal stresses and the temperature distribution across the blade crosssection. Because of the great significance of these two parameters which indicate the metallurgical failure limit when the hot incoming gases from the combustion chamber exceedgenerally or locally-the melting point of the alloy. Beginning with the base case when the coolant is air, which represents the embark line to compare the three other cases with it. The von Mises stress is shown in Fig. 5 which clearly indicates that maximum stress is occurring inside the cooling duct. This is because of the large temperature difference between the temperature of the inner side of the stator and the temperature of the flowing coolant fluid causing thermal stress to be increased. On the other hand, the maximum stress in the case of other coolants is much larger than that of air, especially in the case of using Helium as a coolant as shown in Figs 6-8. The maximum percentage increase compared to air is 71% and the minimum is 45% as indicated in Table 3.   The most important parameter in the gas turbine engine is the turbine inlet temperature since it determines the magnitude of the power output. Designers often avoid hitting the maximum temperature of the alloy that the blade is made from. Because the temperature distribution is nonuniform, a hot spot may appear on the surface of the blade and causes thermal failure. According to the aforementioned, the temperature distribution and its contour have a great significance in this study to determine the maximum and minimum temperature occurred and its location to avoid the high and severe hot spot. Fig. 9 shows the temperature distribution in case of using air as a coolant which is the reference case in this study. The value of maximum temperature is approximately the same temperature as the hot incoming gases surrounding the stator blade. The minimum temperature is higher than the coolant temperature entering the cooling channels from the bottom of the blade and it is 663 K in case of using air as coolant gas to minimize the hot spot temperature differences on the blade surface. The performance of the other coolant gases is much better than air where the minimum temperature recorded is 602 K, 609 K and 610 K in the case of Helium, Ammonia, and Steam consequently as shown in Figs 10-12. The minimum temperature difference of the multiple coolant gases compared to the minimum temperature difference in case of air is shown in Table 4. The cooling effect as the convection process continues from the entering to exiting sections of the coolant gases is decreasing as the heat transfers from the hot wall to the cold fluid. Also, this reduction in cooling effect can be seen across the top view of the stator blade where the maximum temperature and hot spots tend to appear at the trailing edge of the stator while the leading edge has a moderate average temperature in general as shown in Fig. 13. This indicates that the mass flow rate of coolant gas is inadequate to cover all zones in the stator blade and to eliminate the hot spot at the trailing edge; the mass flow rate should be increased to overcome the high temperatures. Any increase in mass flow rate or the bleeding from the compressor may lead to a decrease in the efficiency of the gas turbine engine in terms of overall performance parameters, so a good and reasonable compromise should be taken into account. The behavior of three coolant gases is different from that of air as shown in Fig. 14 which shows the temperature distribution along the blade in x-coordinate only from the trailing edge to leading edge. These values do not represent the most minimal values since the latter occurs at different spatial coordinates. The cooling effect as the convection process continues from the entering to exiting sections of the coolant gases is decreasing as the heat transfers from the hot wall to the cold fluid. Also, this reduction in cooling effect can be seen across the top view of the stator blade where the maximum temperature and hot spots tend to appear at the trailing edge of the stator while the leading edge has a moderate average temperature in general as shown in Fig. 13. This indicates that the mass flow rate of coolant gas is inadequate to cover all zones in the stator blade and to eliminate the hot spot at the trailing edge; the mass flow rate should be increased to overcome the high temperatures. Any increase in mass flow rate or the bleeding from the compressor may lead to a decrease in the efficiency of the gas turbine engine in terms of overall performance parameters, so a good and reasonable compromise should be taken into account. The behavior of three coolant gases is different from that of air as shown in Fig. 14 which shows the temperature distribution along the blade in x-coordinate only from the trailing edge to leading edge. These values do not represent the most minimal values since the latter occurs at different spatial coordinates.

Conclusions
Gas turbine stator blade is subjected to severe high temperature and in order to operate it at the safe limit, a cooling process is proposed to eliminate the hot spots appear at the stator surface. In the common operation of the gas turbine engine, bleeding of air is drawn to cool the blade. The air shows a good and reliable performance in cooling the blade, but it still inadequate. According to the results, it can be concluded that: 1) The three different gases show a better scenario of cooling than air, but they increase the von Mises stress in the blade because of a relatively large temperature difference.
2) The Ammonia and Steam show the same performance approximately so the choice of one of them may be determined by economic justification. 3) In all cases mentioned earlier, the trailing edge zone of the stator still suffers from the high severe temperature the situation that indicates insufficient coolant gas mass flow rate. 4) A good compromise is needed to optimize these different factors to get an effective cooling process at justified economic level especially that using a different coolant rather than air, an extra kit of equipment will be incorporated.