Single or double U-tube? Part 1: Thermal aspects

One of the central questions in borefield design is: “Which is better, a single or a double U-tube?” In this article, we will begin to unravel this mystery once and for all by looking at the thermal side of the story.

Single or double? That is the question

In the world of geothermal design, few topics seem as sensitive or as likely to spark debate as the question of using a single or a double U-tube. As soon as you begin to answer this question, you find yourself in a rabbit hole with differing viewpoints and some surprising considerations. Are we talking about thermal or hydraulic aspects? What about practical aspects or innovative probes? Can any general conclusions be drawn?

In this three part series, we will unravel this question once and for all. Today, the focus will be on the thermal aspects of this comparison. In the coming weeks, we will cover the hydraulic and practical elements, as well as unique probe designs such as the separatus, the TurboCollector, and conical probes like the GEROtherm VARIO and FLUX probes.

Thermal aspects

When we talk about the thermal aspects of the question of single or double U-tubes, we need to revisit our discussion on the effective thermal borehole resistance (which you can read more about in our topic specific article). This resistance quantifies how easily heat is transferred from the fluid to the borehole wall and ultimately to the ground.

A good effective thermal borehole resistance can benefit you in one of two ways:

1. You can reduce the total borehole length, making your system more affordable.
2. You can keep the design the same but operate with less extreme temperatures, improving the efficiency of your system and reducing operating costs.

Below is a graphical representation of the different elements that make up this borehole resistance.

In our discussion of single and double U-tubes, the main factor is convective heat transfer, particularly the transition from laminar to turbulent flow. The pipe to grout conductive resistance is also important, since a double U-tube has twice the heat transfer area of a single U-tube and therefore its resistance will be lower.

In the following sections, some key thermal aspects are discussed:

1. The influence of fluid type (e.g. the type of antifreeze)
2. The influence of the thermal conductivity of the grout
3. Consistent performance under varying flow rates
4. Varying fluid properties

Influence of fluid type

The graph below shows the effective borehole thermal resistance for both a single and a double U-tube at various flow rates. As you can see, both graphs display a sharp cut-off at the point where the fluid transitions from laminar to turbulent flow (more information hier). In this transition phase, the convective part of the borehole resistance decreases significantly, causing the total resistance to drop as well.

!Hinweis
Unless stated otherwise, a DN32 pipe, a borehole diameter of 140mm with a length of 100m and a grout with a thermal conductivity of 1.5 W/(mK) are assumed in this article.

!Caution
The graphs below should not be taken as design guidelines, since the outcome also depends on borehole depth, borehole radius, pipe wall thickness, pipe spacing and other factors.

In the graph above, it is clear that this transition occurs at half the flow rate for the single U-tube compared with the double U-tube. This is because, in a double U-tube, the flow is divided between two pipes, whereas in a single probe it passes through only one.

In this case, there is a window (between 0.25 and 0.45 l/s) where the single U-tube shows a lower borehole resistance and therefore delivers better thermal performance than its double U counterpart.

The position of this window depends strongly on the Reynolds number, which is influenced by both temperature (see later) and fluid type. In the graph below, the same comparison is shown for water. Owing to its favourable viscosity, water reaches the turbulent state at very low flow rates.

In this case, the window in which a single U-tube performs better than a double U-tube is very small (<0.15 l/s) and almost non-existent in practice. It can therefore be said that, in the situation above, the double design consistently outperforms the single probe in terms of performance.

Influence of grout thermal conductivity

One aspect that may be surprising is that even the grout thermal conductivity plays a role in this debate. As mentioned at the beginning of this article, the third part of the borehole resistance is the pipe to grout conductive resistance.

Since the energy must travel from the pipe to the borehole wall through the grout, using a grout with higher conductivity (for example 2 W/(mK)) will improve the performance of the system. In the figure below, the same 25% MPG fluid is used as above, but with the grout thermal conductivity reduced to 1 W/(mK), causing the advantage of the single U-tube to disappear.

The reason why there was previously a window in which a single U-tube outperformed a double U-tube was the drop in the convective part of the effective borehole thermal resistance. Now that the grout has a lower conductivity, this resistance plays a dominant role in the overall resistance. Since a single U-tube has only half the heat transfer area of a double U-tube, the transition to turbulent flow is not sufficient to overcome this barrier.

Consistent performance under varying flow rates

Nowadays, more and more heat pumps are modulating, meaning that they operate with a variable flow rate. In the graphs above, it is clear that in such cases the double U-tube design delivers more consistent performance when operating in the laminar range, whereas the single U-tube shows large variations in borehole resistance due to operation in the transient regime. Therefore, although a single U-tube could allow for a smaller borefield design, if the design flow rate lies in the range where a single probe performs better than a double one, the performance under variable flow rates will still be more consistent with a laminar double U-tube design.

!Hinweis
Modulating heat pumps also play an important role in the hydraulic side of this discussion. Stay tuned for part 2 of this article to learn all about it.

Varying fluid properties

As you might recall from a previous article, the fluid properties (and therefore the Reynolds number and the laminar to turbulent transition) vary with temperature. A borefield therefore has different Reynolds numbers during heating (that is, heat extraction) and cooling (that is, heat injection). For a more complete picture, the resistance is shown in the graph below for MPG (25 v/v%) at both 0°C and 16°C, taken as the minimum and maximum average fluid temperatures respectively.

In the graph above, it is clear that a higher fluid temperature causes the transition to turbulent flow to occur at a lower flow rate. This also plays a role in the present discussion, since borefields may be limited either by the maximum or by the minimum average fluid temperature (more on this in our article on the borefield quadrants).

The borefield above is clearly limited by the minimum average fluid temperature of 0°C. To improve this design, we therefore need to decide whether to use a single or a double U-tube with a reference temperature of 0°C. Looking at the graph above (the red and orange lines), it is clear that for a design flow rate between 0.35 and 0.55 l/s the single U-tube has a lower resistance than the double U-tube and could therefore allow for a smaller borefield size.

The borefield above, on the other hand, is clearly limited by the maximum average fluid temperature of 16°C. To improve this design, we need to decide whether to use a single or a double U-tube with a reference temperature of 16°C. Looking at the resistance graph above (the blue and green lines), we see that there is a window between 0.17 and 0.28 l/s in which the single U-tube outperforms the double U-tube.

Fazit

In the article above, we shed some light on the question: “Which is better, a single or a double U-tube?” from a thermal perspective. It is clear that there is no definitive answer, as the outcome depends on the fluid mixture, the temperature and even the grout thermal conductivity. To determine which option is best for your own project, you can rely on GHEtool for an accurate simulation.

The thermal aspects, however, are only part of the discussion. In our next article, we will take a closer look at the hydraulic aspects of the single versus double U-tube debate.

Literaturverzeichnis

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