Finger seal is a new flexible dynamic sealing technology, and its heat transfer characteristics and seepage characteristics are one of the main research hotspots. In this paper, based on the fractal theory, a fractal model of the total thermal conductance of the finger seal considering the heat transfer effect of the contact gap of the rough surface is established, a fractal model of the effective gas permeability of the adjacent finger seals annulus considering the gas slip effect and the temperature change is established, and a finite element calculation method of the two-way thermo-mechanical coupling for the finger seal is proposed. The results show that the solid-phase thermal conductance decreases with the increase of the scale coefficient. When the axial pressure difference is greater than 0.4$$MPa, the rotor speed is greater than 11,000$$r/min, the radial displacement excitation is [0.03$$mm, 0.09$$mm], and the temperature is less than 600$$K, the gas-phase thermal conductance between the finger seal and the rotor shows an increasing trend. The gas-phase thermal conductance of the finger seal and the rotor is always the main position under different working conditions. Under different fractal dimensions, the solid-phase thermal conductance gradually occupies the dominant position. Temperature has a certain effect on the effective gas permeability, and fractal dimension, scale coefficient, and axial pressure difference have less effect on the effective gas permeability. At an axial pressure difference of 0.08$$MPa, the numerical calculation results of the two-way thermo-mechanical coupling calculation method for finger seal are closer to the experimental results, with a maximum error rate of 1.96%. The above results further improve the theoretical research system of the heat transfer characteristics of the finger seal.

指形密封是一种新型柔性动密封技术，其传热特性和渗流特性是主要研究热点之一。本文基于分形理论，建立了考虑粗糙表面接触间隙传热效应的指状密封总热导分形模型，建立了相邻指状密封有效透气率的分形模型建立了考虑气体滑移效应和温度变化的密封环空结构，提出了指形密封双向热力耦合的有限元计算方法。结果表明，固相热导率随着尺度系数的增大而减小。当轴向压差大于0.4时$$MPa，转子转速大于11000$$r/min，径向位移激励为[0.03$$毫米，0.09$$mm]，且温度小于600$$K，指形密封与转子之间的气相热导呈增加趋势。在不同的工况下，指形密封和转子的气相导热始终处于主要位置。在不同的分形维数下，固相热导逐渐占据主导地位。温度对有效透气率有一定影响，分形维数、尺度系数、轴向压差对有效透气率影响较小。轴向压差0.08时$$MPa下，指形密封双向热力耦合计算方法的数值计算结果与实验结果较为接近，最大误差率为1.96%。上述成果进一步完善了指状密封传热特性的理论研究体系。