## 4 Results and Discussion
### Effect of Friction Terms  
The airflow induced by the propagation of compression waves is influenced by frictional effects, leading to viscous dissipation and affecting the waveform changes during propagation. This section investigates the impact characteristics of the frictional effects on the propagation of initial compression waves. To analyze the impact characteristics of the friction terms on compression waves, the friction effects are defined. When the friction terms in the momentum and energy equations only consider the viscous dissipation caused  
Figure 16: The variations in maximum pressure gradient and steepening rate with propagation distance.  
Figure 17: The variation patterns of maximum pressure amplitude and attenuation ratio with propagation distance.  
Figures 19 and 20, respectively, illustrate the characteristic influence of the friction effects on the steepening rate and attenuation ratio.  
Figure 19: The influence of friction terms on the steepening rate: (**a**) no tunnel entrance hood; (**b**) type A tunnel entrance hood; (**c**) type B tunnel entrance hood.  
Figure 18: The impact characteristics of friction terms on the propagation of compression waves waveform: (**a**) no tunnel entrance hood; (**b**) type A tunnel entrance hoods; (**c**) type B tunnel entrance hoods.  
When no frictional effects are considered, the steepening rate for three different waveforms all continue to increase steadily, with no attenuation observed in the amplitude of the compression waves. The attenuation ratio remains constant at a value of 1. When steady friction effects and both friction effects are considered, the attenuation ratio of the compression waves exhibits a quasilinear decreasing trend, indicating the presence of viscous dissipation during the propagation of compression waves. When adding steady friction, the steepening rate initially increases to reach a maximum value, after which it remains nearly constant overall. When the unsteady frictional effects and both frictional effects are considered, the steepening rate exhibits a trend of initially increasing and then decreasing. However, for the unsteady frictional effects, the amplitude of the compression waves shows almost no attenuation. The steady frictional effect tends to decrease the amplitude of the compression waves while having little influence on the variation in the pressure gradient of the compression waves. This indicates that the steady frictional effect on compression waves does not exert sufficient inhibitory action on their nonlinear effects. Unsteady friction effects cause a significant alteration in the pressure gradient of compression waves propagating in tunnels, indicating that the unsteady friction effects inhibit the nonlinear steepening of compression waves. When both friction effects are present, there are significant alterations in the waveform of the compression waves during  
Figure 20: The influence of friction terms on the attenuation ratio: (**a**) no tunnel entrance hood; (**b**) type A tunnel entrance hoods; (**c**) type B tunnel entrance hoods.  
propagation. These changes stem not only from the steady frictional affecting pressure amplitude but also from the unsteady frictional altering of the pressure gradient of the compression waves.  
Full-scale experimental research shows that in the propagation of compression waves, there is not only attenuation in the pressure amplitude but also a steepening critical distance. Therefore, qualitatively, it can be determined that both types of friction effects must be considered when studying the propagation of the compression waves.