In the last chapter, we investigated the question: “Which is better: a single or a double U-tube?” from a thermal perspective. In this chapter, we use the knowledge from Part 4 of this course to examine the same question from a hydraulic perspective.
Aspectos hidráulicos
When discussing the hydraulic aspects related to the choice of geothermal heat exchanger, the focus lies on the pressure drop of the system. As discussed in Part 4.1, this pressure drop consists of both local losses (bends, junctions, etc.), mainly in the horizontal part of the system, and friction losses, which are an inherent aspect of fluid flowing through pipes. In order to keep the pump power and corresponding electricity consumption low, a low pressure drop is preferred.
The total pressure drop across the borehole is defined as:$$\Delta P = \left(f\cdot \frac{L}{D}+\sum{K}\right)\cdot \frac{\rho v^2}{2}$$where $\Delta P$ is the pressure drop in (Pa), $f$ is the dimensionless Darcy-Weisbach friction factor, $L$ is the length of the pipe in (m), $D$ is the diameter of the pipe in (m), $\sum{K}$ is the sum of all local loss factors, and $\rho$ and $v$ are respectively the fluid density in (kg/m³) and the fluid velocity in (m/s).
- $\Delta P \propto \dot{Q}^2$ (with $\dot{Q}$ is the flow rate in (m³/s))
- $\Delta P \propto D^{-5}$
Both relationships will play a central role in the discussion below.
Secondly, in Part 4.2, the pump electricity consumption was defined as:$$E_e=\frac{\sum\limits_{i=0}^{8760 n}{\dot{Q}(i)\cdot 1000\Delta P(i)}}{n\eta}$$where $E_e$ is the pump electricity consumption in (kWh/year), $n$ is the number of years, $\dot{Q}(i)$ is the flow rate at hour $i$ in (m³/s), $\Delta P$ is the pressure drop at hour $i$ in (Pa), and $\eta$ is the pump efficiency.
In order to answer the question at hand from a hydraulic perspective, the following comparisons will be made in the next sections:
- Same pipe diameter but a different number of pipes
- Different pipe diameter and the same number of pipes
- Different pipe diameter and different number of pipes
Lastly, the pump electricity consumption will be discussed in the light of the single versus double U-tube.
All simulations below are performed using a borehole with a depth of 100 m and a buried depth of 70 cm. The fluid used is MPG with 25 v/v% at 5°C. All pipes have a PN16 (SDR11) pressure rating. The default pipe diameter is 32 mm. All deviations from the assumptions above are mentioned explicitly below.
Mismo diámetro, distinto número de tubos
As a first step in answering the question of the single versus double U-tube, a straightforward comparison is made between a single and a double DN32 probe. This comparison is shown in the graph below.
As can be seen, the double U-tube always has a lower pressure drop than the single U-tube. This is because, in the case of a single U-tube, 100% of the flow rate passes through that pipe, whereas in the case of a double U-tube each pipe carries only 50% of the total flow rate. Since the pressure drop is quadratically proportional to the flow rate, the single U-tube always has a higher pressure drop.
When the hydraulic results above are compared with their thermal counterpart below, as discussed in the last chapter, it becomes clear that for flow rates up to 0.25 l/s and from 0.45 l/s onwards, the double DN32 is the better solution from both a thermal and a hydraulic perspective. The single U-tube, although having a lower borehole resistance between 0.25 l/s and 0.45 l/s, always has a higher associated pressure drop. Its improved borehole resistance is “paid for” with a worse pressure drop.
Distinto diámetro, mismo número de tubos
When taking a short detour and comparing two single U-tubes with different diameters, we can clearly see that the single DN40 outperforms the DN32 case by showing a lower pressure drop. This is because, with a larger internal diameter, the pressure drop decreases with the fifth power of the diameter.
When this graph is again compared with its thermal counterpart, there is an overlapping region, below 0.2 l/s and above 0.3 l/s, where the single DN40 outperforms the single DN32 from both a thermal and a hydraulic perspective.
Diferentes diámetros y número de tubos
Given the insights above, let us revisit the single versus double U-tube discussion, this time with different pipe diameters. Below, the pressure drop is shown for a comparison between a single DN32, a single DN40 and a double DN32 U-tube.
It is clear that there is a range between 0.1 and 0.25 l/s in which the single DN40 has a lower pressure drop than its double DN32 counterpart. Although this might seem counterintuitive at first, since the flow velocity is indeed higher in the DN40 case, the larger pipe diameter results in a smaller contact area between the pipe wall and the fluid, leading to an overall lower pressure drop in this laminar range.
Interestingly, when we compare this again with the thermal side of the story, we can see that there is no longer any overlapping region where the single DN40 outperforms on both the thermal and hydraulic fronts. When it has the lowest pressure drop (<0.25 l/s), the effective borehole thermal resistance is worse and, when the latter becomes the better option (0.3–0.45 l/s), the pressure drop is higher. In contrast, for flow rates above 0.45 l/s, the double DN32 performs better from both a thermal and a hydraulic perspective.
Pump energy and modulating heat pumps
Pressure drop is important for pump selection and for ensuring that the borefield can actually operate under the conditions for which it was designed, but it is only part of the story. The other side is the pump electricity consumption. With a higher pressure drop, the pump consumes more electricity, leading to higher operational costs. In the table below, a comparison is made between the single DN32, single DN40 and double DN32 probes.
For the given flow rate of 0.3 l/s, it is clear that the single DN32 has a significantly higher pressure drop and therefore also a higher yearly electricity consumption compared with the other two options. This can be explained by the higher Reynolds number, which already indicates a turbulent or transient flow regime. As discussed earlier, the single DN40 has a lower pressure drop than the double DN32 case, with a corresponding lower electricity consumption, although the flow velocity is higher, as indicated by the higher Reynolds number.
Historically, this would have been the end of the story. However, since modern heat pumps are increasingly modulating, the flow rate through the borehole is no longer constant, as discussed in Part 3.3. This means that if 0.3 l/s is the design flow rate, most of the time the actual flow rate will be around 70% of that, i.e. 0.21 l/s. The situation for this flow rate is shown in the table below.
It can be seen from the table above that the actual electricity consumption is lower in all cases, but most notably for the single DN32. It still shows the highest value, yet it is already more acceptable than at the design flow rate.
In the next section, a real-life example in GHEtool Cloud will be presented for the case of an auditorium building with these three different probe designs and both a variable and a constant flow rate.
Example in GHEtool
In the sections below, a comparison is made between a single DN32, single DN40 and double DN32 for an auditorium building with active cooling. This comparison is carried out for both a variable flow rate and a constant flow rate.
Simulation with variable flow rate
The graph below shows the hourly temperature profile for a geothermal borefield serving an auditorium building. The simulation was performed using a double DN32 U-tube with a variable flow rate and a constant temperature difference of 4°C across the borefield in both heating and cooling modes.
Since the peak cooling demand (90 kW) is significantly higher than the peak heating demand (30 kW), the cooling demand is actually the limiting factor here, both thermally and hydraulically, with a flow rate of 6.79 l/s through the entire borefield compared with 1.64 l/s for extraction. The pressure drop during cooling is 119 kPa in this case, whereas it is only 13.58 kPa during heating.
The hourly pressure drop graph below clearly shows that, because of the variable flow rates, the pressure drop is significantly lower most of the time (10 kPa or lower). Therefore, the estimated pump electricity consumption is around 37 kWh/year.
When the same simulation is performed for a single DN32 probe, the pressure drop becomes much higher, reaching 386 kPa during injection and 29 kPa during extraction. This is because 100% of the 6.79 l/s now flows through just a single U-tube. The estimated yearly pump electricity consumption in this case is 83 kWh/year. The hourly pressure drop graph for this single U-tube case is also shown below, where it is clear that the pressure drop peaks are significantly higher, although the average pressure drop is again much lower.
The case for the single DN40 is rather similar to that of the double DN32, with a maximum pressure drop of 133 kPa and an estimated pump electricity consumption of 32 kWh/year, which is lower than for the double DN32 case. As discussed above, due to the lower flow rate during extraction, both situations (single DN40 and double DN32) are in the laminar regime, meaning that the single DN40 has a lower pressure drop in this case. Over an entire year, this results in a lower electricity consumption.
Simulation with constant flow rate
As a final comparison, the same three simulations were now performed using the design flow rate of 6.79 l/s as a constant flow rate. The hourly pressure drop graph for the double U-tube is shown below.
Since the flow rate is now constant, the overall electricity consumption is 8079 kWh/year, instead of 37 kWh/year for the case of a variable flow rate. The maximum pressure drop is now 145 kPa.
For the single DN32, the situation is even worse, with a maximum pressure drop of 481 kPa and a total pump electricity consumption of 26734 kWh/year, which is four times the electricity required for heating the auditorium. Because the load is almost never zero, the pump is almost always operating, leading to very high electricity consumption.
For the single DN40, the maximum pressure drop when working with a constant flow rate was 165 kPa, and the pump electricity consumption was 9172 kWh/year.
Conclusión
In this chapter, the question “Which is better: the single or the double U-tube?” was discussed from a hydraulic perspective. When keeping the pipe diameters identical, a double U-tube always has a lower pressure drop than its single counterpart. This implies that there are flow ranges in which the double U-tube is advantageous from both a thermal and a hydraulic perspective.
When working with different diameters and comparing a single DN40 with a double DN32, the situation becomes slightly more complex. In this case, there are flow ranges where the single DN40 has the lowest pressure drop, although not the lowest borehole resistance. There was no range in which a single U-tube performed better both thermally and hydraulically, since the benefits of turbulence are offset by a higher pressure drop.
The comparison of these three probe configurations in GHEtool Cloud for an auditorium building once again illustrates the importance of using a variable flow rate when designing borefields, as well as how small the difference in pump electricity consumption between a single and a double U-tube can be when compared with the overall electricity demand for heating and cooling.