. Results The model used for the fo

. Results
The model used for the following simulations was validated against a cylindrical source model, as well as by comparison with the models developed by Kujawa et al. [35] and Bu et al. [2]. A more specific breakdown of the model validation is detailed in Templeton et al. [34]. Additionally, the proposed model simplifies the velocity profile of the fluid within the heat exchanger to a uniform profile.This assumption was considered due to the laminar nature of the flow, the relatively low fluid velocity, and comparison with results obtained from implementing a parabolic velocity profile for the fluid in the inner pipe and outer annulus. By verifying the Reynolds number of mass flow rates considered in the investigated scenarios,it was concluded that the fluid flow remains in the laminar region.In order to satisfy the no-slip condition for the inner pipe as well as to have a maximum velocity equal to double the mean velocity,Equation (2) was introduced to form the correct velocity profile.where VInner.pipe is the velocity within the inner pipe of the heat exchanger,VInner is the average velocity within the inner pipe of the heat exchanger, and rInner.pipe is the inside radius of the inner pipe of the heat exchanger. Equation (3) was developed by integrating the average velocity flowing through the annulus over the cross sectional area of the annular region of the heat exchanger where VAnnulus is the velocity within the annulus of the heat exchanger,VAnnulus is the average velocity within the annulus of the heat exchanger, and r1 and r2 are the inner and outer radii of the annulus, respectively. Replacing the uniform velocity profile with Equations (2) and (3) in the inner pipe and annulus, respectively, it is possible to investigate the effect of assuming a uniform velocity profile within the heat exchanger (c.f. Fig. 3). As can be observed in Fig. 3, the uniform velocity is a reasonable assumption due to the minor temperature difference observed between itself and the parabolic velocity profile (less than 3% relative difference). The most significant difference is a 0.6 C difference in outlet temperature during the injection cycles.In order to ascertain the validity of this model for applications to geothermal energy storage, the model is compared with the results obtained from a TRNSYS model [29]. TRNSYS operates with an extensive library of components that can be modelled to evaluate temperature profile over a 20 year period than the Eslami-nejad et al. [29] model. The main differences between the two models that could lead to such a difference have been narrowed down to the nature of the heat exchanger that is simulated, the differences in physical configurations, and assumptions made within the model. Due to the higher cross sectional area used for fluid flow in the double pipe heat exchanger design compared to the double utube configuration as well as the insulated inner pipe on the double pipe configuration, the double pipe heat exchanger has a clear ef-ficiency advantage over the double u-tube heat exchanger in this scenario. The efficiency of the heat exchanger is not accountable for the entire difference in outlet fluid temperatures however, as the physical configuration of the system is also important. Eslami-nejad et al. [29] make use of a heat exchanger that is capable of storing and extracting thermal energy simultaneously, while it is impossible to accomplish such a feat with a double pipe heat exchanger.The TRNSYS DST model utilized by Eslami-nejad et al. [29] simplifies the heat transfer from the working fluid of the u-tube to the ground by way of a thermal resistance relation (i.e. analytical solution),and the heat transfer in the remainder of the model is calculated with a finite difference method. Additionally, the TRYNSYS DST model assumes that the heat flux through the boundaries surrounding the heat exchanger is zero. The finite element model proposed in this work assumes that the far boundaries surrounding the heat exchanger are at a constant temperature, and therefore provide a heat flux to resupply the exploited volume of earth with geothermal energy. The outlet temperature profile provided by Eslami-nejad et al. [29] highlights only one data point for every year's worth of data, which is a highly simplified summary of the realistic outlet temperature profile (c.f.Fig. 4). The profile for the proposed model (equivalent total energy/ energy rate) in Fig. 4 demonstrates the seasonal variability that such a system has, with the outlet temperature during the summer phase accentuated due to the thermal energy from solar/cooling being dumped during the five month period. Because a year's worth of solar energy is injected during the summer phase of the total energy scenario for the proposed model, it is as if the solar collector for the proposed model is larger (i.e. same amount of solar energy stored but increased solar thermal power) than that assumed by Eslami-nejad et al. [29]. Because the proposed model can only inject solar thermal energy during the summer phase, compared to year round injection by the double u-tube model,there will be more significant capital costs associated with a larger solar collector for such an equivalent total energy scenario for the proposed model. Furthermore, the solar thermal energy storage during the summer will decrease the effectiveness of the borehole to provide cooling. However, these scenarios are based on a cold climate where heating is prioritized over cooling.It is worthwhile to investigate the effect of the energy storage rate (i.e. identical solar collector size) on the proposed model (c.f.Fig. 4- Proposed model (equivalent energy rate)). The rate of solar energy injection was determined over the summer period, which can be combined with the thermal energy supplied from space cooling to provide a summer rate of thermal energy injection equivalent to Eslami-nejad et al. [29]. Comparing the equivalent total energy and energy rate scenarios, there is little change on the lowest outlet fluid temperature and quite a noticeable change in the peaks of the outlet fluid temperatures. The change in the peak temperatures can be attributed to the decrease in power of the thermal energy that is injected into the double pipe heat exchanger.In order to ascertain the effect that solar injection might have on the long term outlet temperature of a geothermal system, a constant energy extraction model was set up with varying magnitudes of thermal solar injection. The scenarios presented in Fig. 4 correspond to a constant mass flow rate (i.e. independent of energy injection/extraction rates). The average outlet temperatures in the following figures are calculated based only on the outlet temperatures during the extraction phases of the year, so as to isolate the effects of extraction from the effects of injection. Additionally, the linear correlation of COP with the outlet temperatures associated with geothermal extraction can be used to approximate the whole system. From Fig. 5, it is obvious that the injection of solar thermal energy over the summer period results in an overall positive effect on the outlet temperature of the double pipe heat exchanger during the winter period. Increasing the thermal solar injection rate has the effect of increasing the outlet temperature of the working fluid as well as increasing the sustainability of the geothermal system. It is of particular importance to note that for an 1800 W solar thermal injection rate, the average outlet temperature remains relatively stable over 13 years (c.f. Fig. 5). Comparing the 1800 W injection scenario with the no injection scenario, it is clear from the average outlet temperature that the lack of solar injection results in a less sustainable geothermal system. By injecting 1800 W of solar thermal energy during the 5 summer months of the year, the average outlet temperature can be improved by 5% over the 13 year period. Logically, it follows that increasing the rate of heat extraction from a geothermal resource will result in diminishing outlet temperatures over time (c.f. Fig. 6). This hypothesis is demonstrated in Fig. 6, where varying rates of heat extraction are investigated without the aid of solar thermal injection. The sustainability of the geothermal resource is substantially reduced as increasing heat loads are applied (c.f. Fig. 6). The continual decrease in the average outlet temperature illustrates the fact that solar thermal injection can be used to increase the sustainability of a geothermal resource.It is important to note that a steady state is attained quicker for smaller extraction rates. For example, the 2000 W extraction rate will reach a plateau significantly sooner than the 4000 W extraction rate. For each of the scenarios in Fig. 6 the average outlet temperature has reached a pseudo-steady state, meaning that there is a minimal decrease in the average outlet temperature of the working fluid. The magnitude of the extraction rate will be dependent on the specific needs necessary to the situation.To investigate the influence of the working fluid's mass flow rate on the thermal storage capacity of the geothermal resource,various mass flow rates were investigated during the injection cycle of the system (i.e. summer period) while the mass flow rate during the extraction cycle were left constant. A slower mass flow rate through the double pipe heat exchanger allows the fluid more time to transfer the solar thermal energy to the geothermal resource. The transfer of thermal energy is aided by the thermally depleted volume of earth immediately surrounding the borehole,creating a larger temperature gradient. There is significant advantage to decreasing the mass flow rate of the working fluid as evidenced in Fig. 7. The decreased mass flow rates during the injection cycles lead to a 3.7% increase in average outlet temperature,which means that there is more efficient transfer of

ผลลัพธ์ (คลิงออน) 1:

. ghot'e' The model used for the following simulations was validated against a cylindrical source model, as well as by comparison with the models developed by Kujawa et al. [35] and Bu et al. [2]. A more specific breakdown of the model validation is detailed in Templeton et al. [34]. Additionally, the proposed model simplifies the velocity profile of the fluid within the heat exchanger to a uniform profile.This assumption was considered due to the laminar nature of the flow, the relatively low fluid velocity, and comparison with results obtained from implementing a parabolic velocity profile for the fluid in the inner pipe and outer annulus. By verifying the Reynolds number of mass flow rates considered in the investigated scenarios,it was concluded that the fluid flow remains in the laminar region.In order to satisfy the no-slip condition for the inner pipe as well as to have a maximum velocity equal to double the mean velocity,Equation (2) was introduced to form the correct velocity profile.where VInner.pipe is the velocity within the inner pipe of the heat exchanger,VInner is the average velocity within the inner pipe of the heat exchanger, and rInner.pipe is the inside radius of the inner pipe of the heat exchanger. Equation (3) was developed by integrating the average velocity flowing through the annulus over the cross sectional area of the annular region of the heat exchanger where VAnnulus is the velocity within the annulus of the heat exchanger,VAnnulus is the average velocity within the annulus of the heat exchanger, and r1 and r2 are the inner and outer radii of the annulus, respectively. Replacing the uniform velocity profile with Equations (2) and (3) in the inner pipe and annulus, respectively, it is possible to investigate the effect of assuming a uniform velocity profile within the heat exchanger (c.f. Fig. 3). As can be observed in Fig. 3, the uniform velocity is a reasonable assumption due to the minor temperature difference observed between itself and the parabolic velocity profile (less than 3% relative difference). The most significant difference is a 0.6 C difference in outlet temperature during the injection cycles.In order to ascertain the validity of this model for applications to geothermal energy storage, the model is compared with the results obtained from a TRNSYS model [29]. TRNSYS operates with an extensive library of components that can be modelled to evaluate temperature profile over a 20 year period than the Eslami-nejad et al. [29] model. The main differences between the two models that could lead to such a difference have been narrowed down to the nature of the heat exchanger that is simulated, the differences in physical configurations, and assumptions made within the model. Due to the higher cross sectional area used for fluid flow in the double pipe heat exchanger design compared to the double utube configuration as well as the insulated inner pipe on the double pipe configuration, the double pipe heat exchanger has a clear ef-ficiency advantage over the double u-tube heat exchanger in this scenario. The efficiency of the heat exchanger is not accountable for the entire difference in outlet fluid temperatures however, as the physical configuration of the system is also important. Eslami-nejad et al. [29] make use of a heat exchanger that is capable of storing and extracting thermal energy simultaneously, while it is impossible to accomplish such a feat with a double pipe heat exchanger.The TRNSYS DST model utilized by Eslami-nejad et al. [29] simplifies the heat transfer from the working fluid of the u-tube to the ground by way of a thermal resistance relation (i.e. analytical solution),and the heat transfer in the remainder of the model is calculated with a finite difference method. Additionally, the TRYNSYS DST model assumes that the heat flux through the boundaries surrounding the heat exchanger is zero. The finite element model proposed in this work assumes that the far boundaries surrounding the heat exchanger are at a constant temperature, and therefore provide a heat flux to resupply the exploited volume of earth with geothermal energy. The outlet temperature profile provided by Eslami-nejad et al. [29] highlights only one data point for every year's worth of data, which is a highly simplified summary of the realistic outlet temperature profile (c.f.Fig. 4). The profile for the proposed model (equivalent total energy/ energy rate) in Fig. 4 demonstrates the seasonal variability that such a system has, with the outlet temperature during the summer phase accentuated due to the thermal energy from solar/cooling being dumped during the five month period. Because a year's worth of solar energy is injected during the summer phase of the total energy scenario for the proposed model, it is as if the solar collector for the proposed model is larger (i.e. same amount of solar energy stored but increased solar thermal power) than that assumed by Eslami-nejad et al. [29]. Because the proposed model can only inject solar thermal energy during the summer phase, compared to year round injection by the double u-tube model,there will be more significant capital costs associated with a larger solar collector for such an equivalent total energy scenario for the proposed model. Furthermore, the solar thermal energy storage during the summer will decrease the effectiveness of the borehole to provide cooling. However, these scenarios are based on a cold climate where heating is prioritized over cooling.It is worthwhile to investigate the effect of the energy storage rate (i.e. identical solar collector size) on the proposed model (c.f.Fig. 4- Proposed model (equivalent energy rate)). The rate of solar energy injection was determined over the summer period, which can be combined with the thermal energy supplied from space cooling to provide a summer rate of thermal energy injection equivalent to Eslami-nejad et al. [29]. Comparing the equivalent total energy and energy rate scenarios, there is little change on the lowest outlet fluid temperature and quite a noticeable change in the peaks of the outlet fluid temperatures. The change in the peak temperatures can be attributed to the decrease in power of the thermal energy that is injected into the double pipe heat exchanger.In order to ascertain the effect that solar injection might have on the long term outlet temperature of a geothermal system, a constant energy extraction model was set up with varying magnitudes of thermal solar injection. The scenarios presented in Fig. 4 correspond to a constant mass flow rate (i.e. independent of energy injection/extraction rates). The average outlet temperatures in the following figures are calculated based only on the outlet temperatures during the extraction phases of the year, so as to isolate the effects of extraction from the effects of injection. Additionally, the linear correlation of COP with the outlet temperatures associated with geothermal extraction can be used to approximate the whole system. From Fig. 5, it is obvious that the injection of solar thermal energy over the summer period results in an overall positive effect on the outlet temperature of the double pipe heat exchanger during the winter period. Increasing the thermal solar injection rate has the effect of increasing the outlet temperature of the working fluid as well as increasing the sustainability of the geothermal system. It is of particular importance to note that for an 1800 W solar thermal injection rate, the average outlet temperature remains relatively stable over 13 years (c.f. Fig. 5). Comparing the 1800 W injection scenario with the no injection scenario, it is clear from the average outlet temperature that the lack of solar injection results in a less sustainable geothermal system. By injecting 1800 W of solar thermal energy during the 5 summer months of the year, the average outlet temperature can be improved by 5% over the 13 year period. Logically, it follows that increasing the rate of heat extraction from a geothermal resource will result in diminishing outlet temperatures over time (c.f. Fig. 6). This hypothesis is demonstrated in Fig. 6, where varying rates of heat extraction are investigated without the aid of solar thermal injection. The sustainability of the geothermal resource is substantially reduced as increasing heat loads are applied (c.f. Fig. 6). The continual decrease in the average outlet temperature illustrates the fact that solar thermal injection can be used to increase the sustainability of a geothermal resource.It is important to note that a steady state is attained quicker for smaller extraction rates. For example, the 2000 W extraction rate will reach a plateau significantly sooner than the 4000 W extraction rate. For each of the scenarios in Fig. 6 the average outlet temperature has reached a pseudo-steady state, meaning that there is a minimal decrease in the average outlet temperature of the working fluid. The magnitude of the extraction rate will be dependent on the specific needs necessary to the situation.To investigate the influence of the working fluid's mass flow rate on the thermal storage capacity of the geothermal resource,various mass flow rates were investigated during the injection cycle of the system (i.e. summer period) while the mass flow rate during the extraction cycle were left constant. A slower mass flow rate through the double pipe heat exchanger allows the fluid more time to transfer the solar thermal energy to the geothermal resource. The transfer of thermal energy is aided by the thermally depleted volume of earth immediately surrounding the borehole,creating a larger temperature gradient. There is significant advantage to decreasing the mass flow rate of the working fluid as evidenced in Fig. 7. The decreased mass flow rates during the injection cycles lead to a 3.7% increase in average outlet temperature,which means that there is more efficient transfer of