Abstract: A new Liu-Du thermal mixing efficiency formula was proposed to overcome the shortcoming ofthe widely used Liu-Xie thermal mixing efficiency formula in the case with internal heat source(such as after-burning). The Liu-Du thermal mixing efficiency formula can be used to investigate the mixing process within theintegrated afterburner for both the non-after-burning and after-burning case. Through analyzing the detailedequation，the Liu-Du thermal mixing efficiency formula was validated by the physical theory. Besides，the Liu-Du thermal mixing efficiency formula was compared with the Liu-Xie thermal mixing efficiency formula for thenon-after-burning case. By using the Liu-Du thermal mixing efficiency formula，the influence of lobe inward penetration angle on the mixed flow field was studied. When the lobe inward penetration angle increased，the magnitude of the Liu-Du thermal mixing efficiency is found to be enhanced for the mixed flow field near the outletcross section. In the outlet cross section of the integrated afterburner，Liu-Du thermal mixing efficiency of thecase with a lobe inward penetration angle of 25° has a magnitude of 0.779 and the magnitude has augmented10.9% as compared with the 0° case.

Key words: Liu-Du thermal mixing efficiency formula；Integrated afterburner；After burning；Internal heat source

摘要： 为了解决国内外普遍使用的刘 -谢热混合效率公式不能适用于有内热源流场(如加力燃烧)的问题，提出了一种新型的刘 -杜热混合效率公式。该公式能够同时适用于有无内热源工况(如加力和非加力燃烧)下热混合效率的计算分析研究。基于公式推演结果，对新型热混合效率公式的取值极限进行了理论验证。通过同一非加力状态下与刘 -谢热混合效率公式的对比分析，验证了新型热混合效率公式的正确性。接着，利用该公式研究了一体化加力燃烧室加力燃烧工况下波瓣混合器内扩张角对流体掺混过程的影响规律。在混合的后半段区域中，随着波瓣内扩张角增加，同一截面上混合流体对应的刘 -杜热混合效率逐渐上升。在出口截面上，内扩张角 25°模型对应的刘 -杜热混合效率为 0.779，相对于内扩张角 0°模型增加了 10.9%。

关键词: 刘 -杜热混合效率公式；一体化加力燃烧室；加力燃烧；内热源