<p>The requirements of higher efficiency and power output of advanced gas turbine engines push temperature at the turbine inlet to keep growing continuously, which cause the working environments of high temperature components like turbine blade become very severe. Higher temperature also makes the interaction between solid region and flow region stronger. Considering heat conduction within solid region is indispensable for designing of advanced cooling structures. Adjoint method has the advantage that computational cost of gradient is independent with the number of design variables. This feature makes it wildly applied in complicated optimization problems. Study of adjoint based optimization method for heat conduction problems in solid region is of great importance for improving performance of cooling structures as well as building a fully coupled optimization system.</p><p>In this paper, adjoint equation and boundary conditions for three typical heat conduction boundary conditions are derived in detail based on the grid coordinate variation technique. Heat conduction equation and the corresponding adjoint equation are solved using OpenFOAM laplacianFoam solver. A heat conduction optimization system was built based on the Quasi-Newton optimization method. In order to verify the correctness of the optimization system, inverse designs for linear and nonlinear conduction problems within a hollow cylinder were performed. Radius and shape of the inner circle were chosen as design variables. Calculated derivative gradient of temperature with respect to design variables using adjoint method was compared with finite difference results and theoretic results. Then a CHT calculation for C3X cascade using ANSYS FLUENT was conducted in order to get the conduction boundary condition. Numerical simulation results were validated against the experiment results. 2D inverse design of the thickness of a hollow blade was performed. The blade profile was consistent with C3X while two struts were used to separate the inner space of the blade into three internal cooling channels. The result demonstrated the ability of the optimization system to handle inverse design problems within turbine blades. Finally, 2D and 3D optimization of the mean temperature of a hollow blade were also studied based on the assumption that heat transfer coefficients within the cooling hole walls keep constant. The place and width of the struts were optimized in order to reduce the mean temperature. The design variables were kept vary within a given range during the optimization. It could be observed that the optimized structure can cool the blade more effectively and generate a lower temperature profile. It was indicated that the optimization system built in this paper was able to handle inverse and direct design problems within blades and took a step in building a fully coupled adjoint based CHT optimization system.</p>

Adjoint Based Heat Conduction Optimization of Struts Parameters  Within Hollow Blade

Paper Proceedings: https://asmedigitalcollection.asme.org/GT/GT2021/volume/84898

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