Exponential sinusoidal modelling and parameterizing studies for the air temperature waves during underground tunnel ventilation

Air precooling or preheating in underground tunnels is beneficial for reducing air conditioning energy consumption and has been widely used in underground spaces such as hydropower stations and utility tunnels. The fluctuation of the ambient temperature has a significant effect on the precooling and preheating performance of underground tunnels. To explore the fluctuation characteristics of the air temperature in an underground tunnel, field testing was conducted at a hydropower station and an exponential sinusoidal model based on the one-dimensional heat transfer differential equation was established. Comparative analysis has shown that the established model can effectively describe the field air temperature fluctuations in the tunnel. The research results reveal that the air temperature wave propagates along the underground tunnel with a period of 24 h, and the amplitude and average temperature continuously decay from 4.57 °C to 24.87 °C at the tunnel inlet to 0.51 °C and 22.95 °C at the tunnel outlet, respectively, with a delay time of approximately 3 h. Furthermore, the wavelength of the air temperature wave propagating along the underground traffic tunnel is approximately 7912 m, which is longer than the tunnel's actual length of 1000 m. Comparative analysis has verified that the exponential sinusoidal model established in this study has reliable predictive performance, which is beneficial for designing the ventilation and air conditioning system of underground spaces and the utilization strategy of surrounding rock natural energy.