Investigation on heat transfer characteristic and optimization of the cooling air inlet for the twin-web turbine disk

With a higher operation temperature, the conventional aero-turbine single web disk (SWD) has reached its limits. The twin-web disk (TWD) has been designed as a breakthrough, which has an expected performance in weight loss, strength and heat transfer efficiency. However, the lack of investigation on the position of the cooling air inlet is slowing down further application of TWD. Therefore, for a further study, inlet position optimization with maximum average Nusselt number is conducted for TWD flow structure study. The average Nusselt number result shows that the TWD has a better performance in heat transfer. All the works, including modeling and analyzing, can be referred for engineering design. And the conclusions obtained in this paper could be valuable for the future improvement of the TWD.


Introduction
Currently, higher turbine inlet temperature (TIT) has reached 1600K and expected to be pushed toward 2000K in the future, which is beyond the limits of the most parts of aero-engine turbines, especially the first stage turbine (i.e., high pressure turbine, or HPT) disk [1]. The conventional aero-turbine single web disk (SWD) has reached its limit of the AN2 (turbine annulus area multiplied by speed squared, unit m 2 (r/min) 2 ) and thermal loads. As a breakthrough, the twin-web disk (TWD) has been designed with an expected performance in weight loss, strength and heat transfer efficiency. Therefore, it has been proven to be the future trend of the high pressure turbine disk (HPT) by the U.S. IHPTET program [2,3]. Many researchers have studied on the SWD cavity and its discoidal rotor-stator systems using experimental or numerical methods [4][5][6]. Harmand et al. [7] reviewed many convinced numerical technologies during the past decades. In the reference [8][9][10], the decoupled and conjugate methods are widely used. Harmand [7] indicated that the conjugate heat transfer method is an efficient and accurate coupling analysis numerical method and has been widely used in the numerical study on the heat transfer characteristics of gas turbine disk [11][12][13] and other parts of the gas turbine engine [14][15][16] with a desired accuracy. In recent years, optimization based on thermo-fluid analysis is becoming increasingly popular in engineering design [17,18] and turbine disk [19]. In some cases, evolutionary algorithms are used to ensure reaching the global optimum. Besides, thermo-fluid analysis often includes the solution of high nonlinear equations, the cost of time is huge and unacceptable. As a lower fidelity computational model, two-dimensional model is used widely in aerodynamic optimization [20,21] Therefore, the two-dimensional model and structural mesh, which can reduce the cost of the optimization searching by a large margin, are used to find the optimum cooling air inlet position. For the purpose of comparing with the SWD in [22], the models in this study have the same size and boundary conditions. All the works, including modeling and analyzing, can be referred for engineering design.

Geometry model and grid
The 2D dimensional model (fluid region) is shown in Fig. 1 accordingly to Ding's experiment [22]. It is unable to conduct the calculation of 2D model by ANSYS CFX directly. A thin model with only single layer grid in z direction is often used as a solution. Structural grid is also shown in Fig. 1. To ensure that solutions yield sufficient accuracy within CFX, a mesh dependency study has been performed. The average total pressure value and the average temperature are set as the baseline for the mesh independence study based on reference [23]. It is found that the mesh constitutes a satisfying compromise between the duration and the accuracy of the calculation for optimization purpose. The heat transfer on the rim surface consists of two parts: the heat conduction from the heated blade and the heat convection from the high temperature gas. A constant and uniform heat flux is applied here. The detailed boundary conditions are listed in table 1. The layers of near wall mesh are defined as 7 to satisfy the requirement.

Turbulence models
The SST turbulence model is considered a good quality in interface data transition and therefore offers a good compromise between accuracy and calculation cost [7]. In order to obtain a reasonable 3

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The computational result, Y+ is set in a range from 10 to 30 based on the near-wall grid requirement by SST model. Rotational Reynolds number is defined as: (1). Where is the density of the air, is the rotational speed of the disk, R is the radius, is the dynamic viscosity of the air.

Experiments verification
Shuiting et al. [24] have conducted an experiment to investigate the flow and heat transfer on rotor-stator system with pre-swirl angle. Fig.2 shows the configuration of a SWD in the experiment. The data of the SWD sample can be easily obtained from the reference. 1/6 of the rotational computational model in 6 cases (mass flow rate from 200kg/h to 450kg/h) are analyzed for heat transfer by the numerical method above. The numerical result for the temperature distribution of computational SWD ( ) is shown in Fig.3.

Design variable and object function
The dimensionless inlet position x/R is used set as the design variable in a range of 0~0.9. The object is the maximum average Nusselt number Nu ave : (1) Where is the average heat transfer coefficient, R is the disk radius, and is the thermal conductivity of the static fluid. As the only unknown variable, the average heat transfer coefficient can be obtained by the ANSYS CFX. Then the optimization problem can be defined as Maximize .

Optimization technique
Evolution optimization algorithm is a stochastic global search method. The algorithm is operated on a population of potential solutions applying the principle of survival of the fittest to generate better approximations. For each generation, mutation is introduced to reduce the possibility of local optimal search. The evolution strategy here is based on the works of Rechenberg and Schwefel which mutates designs by adding a normally distributed random value to each design variable. The mutation strength (standard deviation of the normal distribution) is self-adaptive and changes during the optimization process [25].

Optimization process
ISIGHT optimization software with ANSYS CFX are adopted here to find optimum designs. The automatic process control is implemented in the windows batch file and windows executable files generated by FORTRAN. The geometry of the model is changed with the changes of geometrical parameters input by the ISIGHT optimizer.

Results
Included mesh generation, CFD analysis, using the 32 core CPU, every optimized step last for about 1.5 min in total. The mean iterations of the computation for thermal-fluid using ANSYS CFX is about 60 and more than 60% of the total time cost. After 51 optimized iterations, the final global optimal results are obtained by evolution optimization algorithm. Fig. 5 shows the optimization history of The object and design variables, which can be easily seen the characteristic of the evolution optimization algorithm. The optimum (x/R = 0.432, Nu ave = 2853.1) is also shown in Fig. 12 in green color. In order to study the sensibility of different inlet positions, the grids and the velocity streamline of 5 models are shown in Fig.6 and 7 respectively. It is obvious that higher inlet position form more vortex in the cavity of TWD, but the velocity loss is also higher. The two aspects brought by the higher inlet position has opposite function on Nusselt number, while the optimum x/R = 0.432 satisfies both aspects.
The Nu ave of TWD with the sequential dimensionless inlet position x/R is plotted in Fig.8, along with the Nu ave data of SWD from the reference [22]. It shows that the optimum inlet positions of SWD and TWD are different. TWD has a higher heat transfer performance in the region of disk hub and a global higher Nu ave in disk surface.

Conclusions
In this paper, a global optimization is conducted with the object of the maximum average Nusselt number. The results show that x = 0.432 is the best position. The Nu ave of TWD and SWD with the sequential dimensionless inlet position x/R also indicate that TWD has a better performance in heat transfer. The works in this paper could be valuable for the future improvement of the TWD.