Research On A Fast Algorithm For The Hourly Simulation Of Inclined Ground Exchangers

Ground source heat pumps(GSHP),a kind of highly efficient and energy saving technology,have been widely used in air-condition systems.The design and performance analysis of a GSHP system usually require simulation of the long-term heat transfer process of the ground heat exchangers(GHEs).However,it is quite time-consuming to complete the hourly simulation with the existing analytical solution of heat transfer model.This paper mainly discusses the heat transfer model outside of the inclined borehole wall.A new model which is more efficient and accurate has been proposed on the basis of previous model.This paper introduced several typical outside and inside heat transfer models of vertical boreholes.Among them,the finite line-source model and the quasi-three-dimensional model can best describe the actual heat transfer process of boreholes.Researchers have proposed a series of improved methods to speed up the calculation of finite line-source model with guaranteed accuracy.The quasi-three-dimensional model can result a more accurate borehole resistance with the optimal p-linear nondimensional average temperature.The inclined borehole is a special form of the vertical borehole.A slight tilt of the boreholes can effectively reduce the interactions between boreholes and improve the theoretical performance of the GHEs so that the use of inclined borehole would have saved the ground surface area or reduced the total borehole length.It is significant to study the transfer model of inclined boreholes.This paper improved the analytical g-function for inclined boreholes by mathematical methods,the improved g-function calculates much faster than the original one.We proposed the new representative temperature of the borehole wall in addition to the middle temperature and integrated mean temperature.In this paper,the practical varying heat flow is approximated by a series of rectangular pulse.We introduced a new thermal response factor called δ-function for a unit rectangular heat pulse.In order to speed up the calculation,the Fast Fourier Transform(FFT)has been used to reform the convolution.The computational accuracy of different thermal response models(g-function,improved g-function,δ-function)are compared and discussed.The three thermal response factors are the exact solution of finite line-source model,the error ofnumerical calculation is mainly related to whether the formula has singularity,the complexity of integral(integral or double integral)and the integral interval.Besides,comparison of error and time consumed of different representative temperature has been presented.The long-term simulation with integral mean temperature is quiet time consuming,while both the middle temperature and the new representative temperature calculate much faster.