Analytical Solution Research And Heat Transfer Analysis Of Mid-deep Underground Heat Exchangers

With the development of society,people have higher requirements for living environment.Currently,building energy consumption gradually increases,which accounts for about 33% of the total social energy consumption so far.But the shortage of fossil fuels has undoubtedly put unprecedented pressure on the energy supply system.Therefore,renewable energy has attracted the attention of many scholars around the world,and provides a feasible solution to the current situation of energy shortage.Compared with other renewable energy sources such as solar energy,tide energy,et al.,geothermal energy has the unique advantages of wider distribution,larger reserves and convenient utilization.The majority of the researches on geothermal energy focus on the application technology of shallow geothermal energy.Although this type of technology is well developed,but the shortcomings are also more obvious,such as the limited available geothermal temperature for heating,the imbalance between heat injection in summer and heat extraction in winter which may cause a cooling/heating load accumulation for heating dominated buildings.By contrast,the deep borehole heat exchanger(DBHE)heating system has the advantages of small occupation area,higher geothermal temperature,good thermal balance,etc.,which creates a new way for rational and sustainable utilization of geothermal energy,especially suitable for heating applications in cold areas,and has been favored by scholars and engineers.At present,most scholars have used numerical method to study the heat transfer of DBHE.However,the deeper borehole depth and the smaller borehole radius require huge number of girds and put big calculation pressure on computers.Therefore,it is difficult to use the numerical method to further study the DBHE with multiple boreholes.In view of this situation,this paper focuses on the establishment of the analytical solution model of the DBHE,and provides analytical solutions of fluid temperature and soil temperature suitable for engineering calculation.First of all,the improved transient thermal resistance of the surrounding soil based on the infinite line source model was introduced and the hypothesis of uniform borehole wall temperature and the heat transfer rate per borehole length in the traditional model was abandoned.According to the conventional models,this model is divided into two parts.The first part is the analytical solution model of variable heat transfer rate per borehole depth with uniform geothermal temperature.The second part is the temperature response caused by the initial temperature of the geothermal gradient without other heating sources.Based on the Laplace transform method and the principle of linear superposition of temperature,the analytical model of the fluid and soil temperature response of the DBHE is obtained.Then the new analytical model was verified with comparison of previous numerical model.To be specific,It has been proved that this model can effectively predict the inlet and outlet water temperature of DBHEs with single borehole.However,this model is not suitable for calculating the multiple deep boreholes because of the none-liner problem in fluid equation.In order to solve the heat extraction problem of the DBHE with multiple boreholes,a new model suitable for analyzing the heat transfer of the DBHE with multiple boreholes is proposed in this dissertation,which adopts the method of combining numerical solution and analytical solution.Considering the characteristics of heat extraction in DBHE,the Finite Difference Method(FEM)was used to calculate the fluid temperature within the borehole,while the analytical solution model was used to calculate the geothermal temperature distribution outside the borehole.The two models were connected together by the variable heat transfer rate on the borehole wall.It has been proved that this model can effectively predict the inlet and outlet water temperature.Finally,based on the new analytical model the effects of ground heat flow,mass flow rate of the fluid,pipe's structure and other parameters on the heat extraction efficiency of DBHE are analyzed.The results show that the DBHE have improved thermal performance with the increasing ground heat flow and mass flow rate of the fluid.Reducing the size of the inner tube is beneficial to reduce the thermal short circuit.In addition,using the principle of temperature superposition,the influence of parameters such as the distance between boreholes on the heat extraction efficiency of DBHE is discussed.The larger borehole distance is suggested to prevent the DBHE from reducing thermal efficiency.The conclusion obtained in this paper can provide a reliable and simple calculation tool for the practical engineering design and simulation of DBHE,which has a certain guiding significance.