Optimizing the clearance dimensions of the gas turbine combustion chambers using the Taguchi method

Nomenclature:

• Introduction

The maintenance of equipment in gas turbine power plants requires cost-effective management due to the significant costs associated with purchasing and repairing them. The compressor, turbine, and combustion chambers constitute the main parts of gas-fired power plants, including expensive components that require meticulous maintenance. Moreover, to keep the combustion chambers safe and enhance the turbine's performance and longevity, it is necessary to prevent thermal stresses caused by high-temperature flows in these two components. Due to inadequate cooling and temperature control, temperatures can rise rapidly, resulting in significant thermal stresses and the destruction of the turbine blades and the ceramic walls of the combustion chamber. The combustion chambers and turbine's temperature can be affected by changes in geometric variables, fuel, and airflow rates. A wide range of research has studied reducing and controlling the temperature of the combustion chamber using various techniques. Film cooling is one of the popular techniques, which was investigated by many researchers. Gollady and Lucas (Golladay RL, 1963) investigated the effect of the film cooling in the combustion chamber of a rocket engine. They studied cooling combustion chambers by using tangential and angled injection. They used propane and nitrogen as coolants. Totten (JK, 1964) examined the effect of multi-row film cooling in a combustion chamber using different coolants, such as hydrogen, methane, and carbon dioxide. He illustrated that the use of several rows is suitable for the cooling system. The results of his experiment also showed that carbon dioxide has a minor impact on combustion chamber cooling compared to the other two coolants. Bunker (RS, 2005) investigated the cooling holes of combustion chambers and concluded that wider gaps decrease cooling by reducing the momentum of the coolant airflow and its mixing with the hot gas flow. Li et al. (Li, Peng, & Liu) numerically studied the cooling performance of a combustion chamber. Their results indicated that injecting a strong cooling jet through holes disturbs a cooling film and, thus, adversely affects the temperature in the combustion chamber wall. Mahdavi Moghaddam and Bahmani (moghadam & Bahmani, 2011) performed a three-dimensional analysis of the effect of the geometry of the cooling holes on the effectiveness of film cooling in a combustion chamber. Based on their analysis, an increase in the length-to-width ratio of the cooling hole could lead to an improvement in film cooling effectiveness for the combustion chamber. Andreini et al. (AntonioAndreini, 2017) experimentally studied the influence of the cooling hole angles on the thermal performance inside the combustion chamber of a gas turbine. They utilized Particle Image Velocimetry (PIV) and Pressure Sensitive Paint (PSP) methods in their study. The results showed that a decrease in the angle improved cooling performance.

Ji et al. (Ji, 2018) empirically investigated the effect of 30° and 90° cooling hole angles on the heat transfer performance in a combustion chamber. Their results revealed that the 30° angle provided better performance than the 90° angle. Jing et al. (Tingting Jing, 2021) examined the impact of the film cooling angle on the cooling efficiency in a supersonic combustion chamber. They illustrated that a decrease in the injection angle improves cooling efficiency. In the following, researchers such as Kim (Kim, 2018), Huang et al. (Huang, 2018), Park et al. (Park, 2019), Wang et al. (J. Wang, Ke Tian, Jing Luo, and Bengt Sundén, 2019), and Dai et al. (Dai, 2021) have investigated the effect of cooling hole geometry on the temperature distribution of combustion chambers. They examined holes with cylindrical, conical, crescent-shaped, and rectangular geometries and concluded that the crescent-shaped holes had the best cooling performance. Liu et al. (Liu, 2020) studied the influence of the hole configuration on cooling performance. Their results show that the hexagonal structure of the holes improved cooling by up to 3.8 times. Wang et al. (J. Wang, Hu, Du, Tian, & Baleta, 2021) investigated film cooling in a gas turbine combustion chamber numerically. They examined different inclination angles to investigate the cooling of the combustion chamber. They also performed numerical simulations based on the combustion chamber of a Can-type gas turbine using propane as fuel. Based on the Reynolds Stress Model (RSM) for turbulence and flame-sustained diffusion of non-premixed combustion, the results illustrated that the cooler provides effective protection for the combustion chamber liner, and reduces temperature by 31.7%. Also, results show that the 30-degree hole slope angle has the most efficient cooling effect. Je et al. (Yongbin Ji, 2022) studied the effect of cooling injection direction on the temperature distribution of a gas turbine combustor. They investigated the effect of three different hole inclinations (30°, 90°, and 150°). Results show that the orthogonal holes present a higher overall cooling effectiveness than the forward ones. Pang et al. (Liyao Pang, 2023) analyzed numerically the effect of the hole diameter on the outlet temperature of a gas turbine combustor.  They represented that low-temperature areas close to the outlet wall expanded when the diameter of cooling holes increase. Bai et al. (Naijian Bai, 2023) investigated experimentally effect of holes arrangement  on the wall temperature of a gas turbine combustor. Results show that dense and uniform holes arrangement can greatly improve cooling performance.

All of the above cooling methods have been created by changing the geometry of the combustion chamber. However, the multi-piece combustion chamber structure inevitably creates clearances and cooling effects that cannot be avoided. The film cooling method created by clearances between the combustion chamber parts is a practical approach to the thermal management of the combustion chambers. The variations in the temperature of the wall combustion chambers change clearances. The difference between the clearances of the two combustion chambers can affect the inlet air flow rate, cooling, and temperature distribution across them, which leads to considerable temperature variations at the combustion chamber outlet and turbine inlet and causes severe damage to the turbine blades. Therefore, clearance dimensions are a crucial parameter to consider at the power plant start-up. In this paper, the four clearance dimensions with four values can be considered for each combustion chamber. The present study aims to investigate the effects of different clearance values on temperature distribution in combustion chambers. The experimental study of all cases is not reasonable. Therefore, first, the Taguchi method was applied  to decrease the number of case studies. Then, the temperature distribution in the combustion chambers of turbine gases will be calculated using CFD simulation. In the end, these clearance dimensions in such a way as to produce the slightest temperature difference at the outlets of the two chambers will be optimized. The equipment modeling, thermal and flow simulation, and optimization will be performed by Solidworks, Ansys Fluent 17, and Taguchi method respectively.

• Geometry and boundary conditions

The main components of the combustion chambers of the v94.2 gas turbines located in the Shahid Kaveh Power Plant of Qaen are depicted in Fig. 1. The combustion chambers form two elbows at the two sides of the center casing (Part 5). Each combustion chamber elbow comprises an annular air inlet (A) and a hot gas space (B). Also, the combustion chamber was built in three pieces to facilitate assembly and disassembly. This multi-piece structure has resulted in clearances between the different parts. The flame tube (4), the burners (2), the mixing chamber (8), and the inner casing (9) are the main components of the chambers as shown in Fig.1. The geometry and dimensions of the combustion chambers are illustrated in Fig. 2. In addition, Fig. 3 shows the airflow path inside the combustion chamber. The compressed air exiting from the compressor enters the combustion chamber via the annular area (white arrow). It moves toward the burners at the top of the combustion chamber. Part of this air enters the combustion chamber directly as cooling air without participating in combustion via the clearances in Regions A and B. Then, the air mixes with the main flow and fuel at the burner region (blue arrow), and the combustion occurs in the flame tube. The combustion products depicted (black arrow) are guided towards the combustion chamber outlet and turbine from the inner casing. The dimensions of the clearances significantly affect the airflow distribution in the combustion chamber. The asymmetry in the values in the two rooms creates different pressure drops and, thus, different airflow rates. The difference in the airflow rate in the two chambers leads to a non-uniform temperature distribution at their outlets, creating hot spots at the turbine inlet. Therefore, clearance dimensions are a crucial parameter to consider at the power plant start-up.

Figs. 4 and 5 illustrate the clearance variables, where s and t represent the clearances between the mixing chamber and the flame tube, respectively. The clearance values between the mixing chamber and the inner casing are denoted by a and c. Table 1 shows the clearance values at four levels for each variable to study their effect on the left-hand-side combustion chamber. For the right-hand-side combustion chamber, a value between of four levels mentioned in Table 1 is considered for each variable. The ranges of the variables at different levels were determined experimentally based on the maximum space between the components of the combustion chambers ("Performance test of Kave combined cycle PP (GT V94.2),").

Fig. 4. Values of clearance between the flame tube and the mixing chamber

 Fig. 5. Values of clearance between the inner casing and the mixing chamber

 Table 1. The clearance values

Table 2 displays the input variables for the problem under the baseload condition. The compressor outlet temperature, fuel, and airflow rates were obtained experimentally from performance test results at the Shahid Kaveh Power Plant in Qaen. To begin the simulation in the software, boundary conditions are adjusted, including the mass flow rate conditions for air and fuel inlet and pressure conditions for the outlet obtained from practical information. Fig. 6 shows the schematic of the combustion unit of the gas-fired power plant with boundary conditions. For a better understanding of the boundary conditions type, the flow direction is present in Figure 7 for each boundary condition.

Table 2. Boundary condition data

Fig. 6. Schematic of the combustion unit of the gas-fired power plant with boundary condition

Fig7. Schematic of direction of flow for each boundary condition

• Simulation and governing equations

To numerically simulate the momentum equations, the SIMPLE algorithm was employed. The combustion flow is turbulent and was modeled using the standard k-ɛ model which is a popular model for simulation of the industry problems.  In this model, two transfer equations are solved to determine the turbulent kinetic energy (k) and the energy dissipation rate (ɛ), as follows(BS, 2007):

where,  represents the turbulence energy generated by changes in the average speed,  denotes the turbulence energy generated by the buoyancy force, and expresses the expansion perturbation in compressible turbulence to the overall turbulence energy dissipation rate. Previous studies (BS, 2007) determined the equation constants at  .

The combustion reaction rate, which appears as a source term in the equations of energy and conservation of the species mass fractions, was calculated using the Magnussen model in the following form(Magnussen, 1977):

where R.R represents the reaction rate, A is an empirical constant equal to 4, Y denotes the fuel and oxygen mass fraction, and S represents the oxygen required to burn 1 kg of fuel under stoichiometric conditions.

In addition, the thermal form, which has been developed by the Zeldovich mechanism (Warnatz, 2006) was considered for the modeling of the nitrogen oxides (NO), and its associated reactions are as follows:

 where    are the forward and backward reaction constants and are expressed as follows(Hanson, 1984):

Thus, the rate of formation of thermal NO is determined as follows("ANSYS ", 2013):

 The DO model ("ANSYS ", 2013) was employed to model radiation. This model is suitable for simulating combustion and approximating the flame temperature.

Figures 8 and 9 show the average outlet temperature of the combustion chamber for the different numbers of grids and the geometry of the combustion chamber and the computational mesh, respectively. As shown, the minimum number of hexagonal elements ensuring the grid independence of the results was determined at 3106000. Also, a convergence criterion of 10^-5 was considered for the variables. Ansys Fluent 17 software was used for the simulation. Based on the immense computations, a computational server with 32 processing cores and RAM of 120 GB was used to carry out the calculations

Fig. 8. The average outlet temperature of the combustion chamber for the different numbers of grids.

Fig. 9. Schematic of the computational mesh of the combustion chamber in the v94.2 turbine

• Taguchi-based optimization algorithm

As mentioned in the previous section, there are four clearance variables in each combustion chamber due to the multi-part nature of the combustion chamber. In addition, four levels were considered for each parameter. Therefore, the total number of clearance cases equals 256. Since it is not economical to study all the subjects given the sizeable computational burden involved, the Taguchi method is used as a common technique to reduce the study cases and optimize a function. This method utilizes an orthogonal array, which can be applied to study many variables using only a small number of cases. The primary motivation for using this technique for optimization in the present research was to reduce the number of study cases and extend the results to the total available space for the design variables. The first step in the Taguchi method is to select the independent variable levels, i.e., the factor levels, as shown in Table 1. By using orthogonal arrays, the second step involves determining the interaction between the independent variable levels. In these arrays, the columns are orthogonal to one another. This means that all the variable level combinations exist for every column pair. The existing orthogonal arrays consist of L4, L8, L9, L12, L16, L18, and L32. To select the orthogonal array, it is necessary to first determine the minimum number of tests using the following method (A. C. Atkinson, 2008):

In this equation, P denotes the number of independent variables, and L_v represents the number of levels for each independent variable. The four variables in this study are divided into four groups, as presented in Table 1. Therefore, the minimum number of tests is 13 based on Eq. (8). Consequently, one may select the orthogonal arrays L16, L18, and L32. The orthogonal array L16 was used in this study. Table 3 shows the structure of the above collection. The total number of possible cases equals 44 based on the values of the variables. The Taguchi optimization algorithm reduces the number of subjects required for the study to 16. Therefore, the Taguchi method was performed in Minitab software to simulate 16 cases, according to Table 3, to determine the optimal variable levels.

Table 3. The configuration of the values of the variables in mm for simulation using the Taguchi algorithm

For data analysis, the Taguchi method employs a statistical performance criterion called the signal-to-noise ratio. The signal-to-noise ratio is a performance criterion that selects the control variable levels so that the noise variables are countered most effectively. The signal-to-noise ratio depends on the quality characteristic criterion to be optimized. Although there are many possible signal-to-noise ratios, the three most common criteria are taken into account. These criteria are used in the following cases:

1. B higher-quality characteristic is better.
2. B lower-quality characteristic is better.
3. B nominal-quality characteristic is better.

Since decreasing the difference in the average temperature between the combustion chambers is the main object of this study, the “smaller-better” is used for the determination of the optimal levels. For this criterion, the following relationship is required to calculate the signal-to-noise ratio of the cases with N  iterations (W.P. Gardiner, 1998):

where X_m represents the difference in the average outlet temperature between the combustion chambers. Also, the signal-to-noise ratio is measured in dB. Given the above equation, it must be noted that the signal-to-noise ratio is defined so that its highest value is always preferred. Hence, the optimal levels have the highest signal-to-noise ratio for each variable. The signal-to-noise ratio of the optimal levels is calculated as follows (W.P. Gardiner, 1998):

where P is the number of independent variables. Finally, the predicted optimal outputs are obtained as follows (W.P. Gardiner, 1998):

• Validation

In Table 4, the average temperature and the average NO_x mass fraction at the combustion chamber outlet from the numerical solutions were compared with the data collected from Kaveh Qaen's power plant ("Performance test of Kave combined cycle PP (GT V94.2),") to validate the accuracy of the results. The working conditions were similar to the regular cycle of the present study. The results revealed that the numerical solution errors were 0.38%, and 1.74% for temperature and NO_x emissions, respectively. Therefore, both results have a good agreement with the empirical results.

Table 4- Comparison of the numerical and Empirical results

6- Results and discussion

6.1. Flow field study

The velocity vectors in the middle section of the combustion chamber are illustrated in Fig. 10. The figure shows that the airflow exits the compressor and moves upward in the combustion chamber. Velocity magnitudes reach up to 2500 m/s near the burners due to a reduction in cross-sectional area. Then, the combustion products move downward from the flame tube and the mixing chamber, pass through the inner casing, and move toward the turbine. Moreover, a magnified image of the velocity vectors around the clearances is depicted in Fig. 11. In both figures, there is a secondary airflow that moves through the passages in the flame tube and inner casing toward the middle and end sections of the combustion chamber. This airflow does not contribute to combustion and plays a role in diluting and cooling the combustion products. The velocity vector magnitudes at the clearance area significantly increase due to a reduction in the cross-sectional area. So its magnitude is about 800 m/s at the upper and about 1500 m/s at the lower clearances.

Fig. 10. The velocity vectors at the middle section of the combustion chamber

Fig. 11. A magnified view of the velocity vectors at the clearance regions

Fig. 12 displays the velocity vectors in the burner region. As shown, the velocity vectors are compact in this region, and the speed reaches 2500 m/s due to flow passing through a small cross-section. Moreover, it can be observed in this region that a rotating flow contributes significantly to the mixing of fuel and air.

Fig. 12. The velocity vectors at the burner region

6.2. The distributions of temperature and mass fraction of the species in the combustion chambers

The temperature distribution in the middle section of the combustion chamber is shown in Fig. 13. According to the figure, the airflow has been preheated by 800 K between the air and burner inlet due to heat transfer from the inner wall. Then, as air and fuel mix and combustion occur, the temperature in the burner area and the flame tube increases significantly. The temperature at the flame area rises to 2200 K. The irradiative heat transfers between the flame and the chamber walls and the subsequent dilution and penetration of diluting air through the clearances reduce the temperature. The air entering from the upper clearances decreases the temperature to 1400°C, which is further reduced to 1200°C at the mixing chamber outlet via the air entering from the lower clearances.

Fig. 13. The temperature distribution at the middle section of the combustion chambers

Fig. 14 shows the oxygen mass fraction distribution in the middle section of the combustion chamber. As can be seen, the mass fraction of oxygen is constant until the airflow reaches the burner area, after which it decreases in the flame tube due to the mixing of oxygen with fuel and combustion. Then, the diluted air entering the mixing chamber via the clearances increases the mass fraction of oxygen. Finally, the oxygen mass fraction in the region between the inner casing and the outlet of the combustion chamber remains nearly constant.

Figs. 15 and 16 show the fuel mass fraction distribution in the middle section and the burner area of the combustion chamber. It is evident that the fuel mass fraction is most significant at the burner inlet then the fuel has been gradually consumed due to mixing with oxygen. As a result of the excess air, a large part of the fuel burns at the burner area, and the mass fraction of fuel decreases with increasing distance from the burner to almost zero.

Fig. 17 shows the carbon dioxide (CO₂) mass fraction distribution in the middle section of the combustion chamber. This figure shows that the CO₂ mass fraction forms after mixing fuel and air. It is at its maximum in the flame area, where the temperature is at its highest. Then, it decreases in the flame tube due to NO_x production. Also, the diluted air in the clearance regions reduces the CO₂ mass fraction. After that, the CO₂ mass fraction is constant until the airflow reaches the combustion chamber outlet.

6.3. Optimization of the difference in the outlet temperatures of the two combustion chambers

The difference between the outlet temperatures of the two combustion chambers must be reduced in gas-fired power plants to produce a uniform temperature distribution across the two combustion chambers and reduce the probability of the creation of hot spots on the turbine blades. In return, the service life of hot components in the combustion chambers and turbine blades will be increased. Fig. 18 displays the temperature distribution at the outlet section for the 16 cases based on the proposed Taguchi method. As shown, the combustion chamber with the higher average clearance has a lower temperature distribution in its corresponding semi-circle in all cases due to receiving a higher mass flow rate and being better cooled. Regardless of the values of the clearance variables, a higher mass flow rate indicates that the average clearance performs as a suitable measure for airflow and temperature distributions in the two chambers.

Furthermore, when the average clearances of the combustion chambers are close together, a visible symmetry between the outlet's temperature distributions at the left and right semi-circles is observed as their temperature difference reduces. In addition, the clearance difference between the two chambers has created hot spots at the combustion chamber outlet. These points, which are sometimes observed at clearance differences of about 1 mm, may damage the turbine blades. This difference indicates that the temperature distribution at the combustion chamber outlet depends on the clearance dimensions.

Fig. 19 shows the role of the variables in minimizing the temperature difference between the two combustion chambers. According to the Taguchi algorithm, a higher signal-to-noise ratio of a variable leads to better performance and in the case of temperature difference between outlets, a higher signal-to-noise ratio would mean that the temperature difference is smaller. Hence, the variable s has the highest effect, as shown in Fig 19. In addition, it is observed that Level 2 of the variable s, which corresponds to the slightest clearance difference between the two combustion chambers, has caused a minor temperature difference. The same is true for the variables a and t. The variable c creates the slightest temperature difference at Levels 2 and 3 since, at these levels, the clearance is equal to that of the right-hand-side combustion chamber.

Fig. 20 displays the influence of the variable s on the distribution of the combustion chamber outlet temperature. As can be seen, an increase in s gradually reduces the outlet temperature of the left-hand-side combustion chamber and increases that of the right-hand-side combustion chamber. The temperature distribution is symmetrical mainly in the third case due to the slight difference between the values of s in the two combustion chambers. In this case, where the average clearance difference between the two chambers is 1 mm, the temperature difference of corresponding points on the left- and right-hand sides of the outlet reaches up to 100°C.

Fig. 21 shows the temperature difference between the two combustion chambers versus changes in the variable s. According to the figure, the slightest temperature difference exists at a thickness of 3 mm, similar to Fig. 19. Moreover, the temperature difference increases with a rise or fall in s beyond 3 mm. This fluctuation is because of an increase or a decrease in the clearance value beyond 3 mm, which increases the clearance difference between the two chambers. As a result, the mass flow rate differs in the two chambers, leading to different temperature distributions. Although the clearance difference corresponding to the variable s is 1 mm for a thickness of 3 mm, there is an average temperature difference of 15°C between the two chambers.

Fig. 18. The temperature distribution at the outlet section for the 16 cases proposed by the Taguchi method

Fig. 19. A comparison of the effects of the variables on reducing the outlet temperature difference.

Fig. 20. The effect of the variable s on the outlet temperature distribution

Fig. 21. The effect of the variable s on the outlet temperature difference

Fig. 22 displays the influence of variable a on the temperature distribution at the combustion chamber outlet. As seen, an increase in this variable gradually reduces the temperature of the left-hand-side chamber due to increasing the flow rate in it. The temperature distribution is symmetrical mainly in the fifth case due to the slight difference between a values in the two chambers and the small difference in the average clearance.

Fig. 23 illustrates the temperature difference between the two chambers based on changes in the parameter of a. The results depict that the least amount of temperature difference of combustion chambers is observed for thicknesses of four millimeters, which is the least amount of clearance parameter a. Similarly, to the case for s, the temperature difference increases with a decrease or increase in the amount of a from four millimeters.

Fig. 22. The effect of the variable a on the outlet temperature distribution

Fig. 23. The effect of the variable a on the average outlet temperature difference at the combustion chamber outlet

7- Conclusion

In this paper, the effect of the dimensions of various clearances in the combustion chamber on the temperature distribution and mass fraction has been numerically studied. The different clearance dimensions were optimized using the Taguchi method in Minitab software to reduce the temperature difference between the two combustion chambers. Following is a summary of the findings of this study.

1. The numerical results exhibited high accuracy, and the results revealed that the numerical solution errors were 0.38%, and 1.74% for temperature and NO_x emissions, respectively.
2. By decreasing the average clearance difference between the two chambers, the average temperature difference at the outlet decreases, supporting that average clearance is a suitable criterion for dampening temperature differences and the creation of hot spots.
3. The combustion chamber with the smaller average clearance created higher temperatures at its corresponding outlet semi-circle. When the average clearance of the combustion chamber decreases by 5 millimeters, the temperature of its corresponding outlet semi-circle decreases around 100°C.
4. The asymmetry in the average clearance significantly contributes to the asymmetry in the temperature distributions of the two chambers, and a difference as small as 1 mm between the average clearances of the chambers can cause a point-for-point temperature difference of as large as 100°C between the left and right semi-circles of the outlet.
5. The variable s of the clearance between the flame tube and the mixing chamber is the most effective variable in controlling the air flow rate, preventing hot spots, and reducing the temperature difference between the two chambers. When the average variable s of the clearance difference between the two chambers is 1 mm, the temperature difference reaches up to 15^oC and 100^oC in average and point mode, respectively.

As shown in this study, the clearance dimensions have a significant impact on the distribution of outlet temperature in the combustion chamber and are a key parameter for power plant startup. Therefore, since turbine blades have temperature limitations, the investigation of the effect of clearance dimensions on the turbine temperature distribution is recommended for future studies.

Conflict of Interest

The authors do not have any conflicts of interest to declare.