Zero-dimensional modeling for transient response of non-adiabatic cavity with single opening
With the present condition that there are errors in predicting transient response of cavity with single opening using the ideal adiabatic cavity model in the presence of heat transfer, a zero-dimensional transient modeling method applied to a single opening cavity with the consideration of the effect of heat transfer on cavity transient response was proposed. In virtue of researching the factors influencing the heat transfer between the gas and the cavity wall, the characteristic equation related to heat transfer was deduced by dimensional analysis, and the concrete function of it was determined by CFD numerical simulation. The heat transfer term which was not considered by adiabatic model of cavity with single opening was expressed explicitly, and a non-adiabatic zero-dimensional transient model of cavity with single opening was established. The model was compared with CFD simulation and the results show that:Good agreement is achieved by comparing the responses of pressure and temperature calculated by non-adiabatic zero-dimensional transient model of cavity with single opening with that calculated by CFD simulation, and the maximum relative error is no more than 0.8%. The accuracy of the model and the feasibility of the modeling method are verified; The maximum relative error between the adiabatic model of cavity with single opening and CFD simulation results is 6%, which indicates that the non-adiabatic model can reflect the real response more accurately than the adiabatic model. In addition, the non-adiabatic model reduces three dimensions within the accuracy of 1% compared with the CFD simulation, and also significantly lowers the computational cost of non-adiabatic cavity with single opening simulation, which can effectively support zero-dimensional transient modeling of cavity with high accuracy in aero-engine air system.
表 1 参数量纲
Table 1. Dimension of parameters
参数 量纲 k ML/(ΘT3) μ M/(LT) ρi M/L3 cp L2/(ΘT2) d L ui L/T Tv Θ h M/(ΘT3)
表 2 初始边界和计算边界条件参数
Table 2. Initial boundary and computational boundary condition parameters
位置 压力/Pa 温度/K t=0 t>0 t=0 t>0 进口 101 325 191 504 288.15 288.15 壁面 323.15 323.15 腔内 101 325 323.15
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