As of today, the turbocollector from Muovitech is available in GHEtool Cloud. In this article, we will shed light on the mathematical model behind the turbocollector and explore the concept of turbulence more generally, based on a recent paper by Niklas Hidman.
Turbocollector
The turbocollector is a product developed by Muovitech. Unlike traditional smooth internal pipe surfaces, the turbocollector features multiple small fins along its inner surface. These fins are oriented in alternating clockwise and counterclockwise directions along the length of the pipe. Acting as passive turbulators, they are designed to induce turbulent flow behaviour at lower flow rates, thereby enhancing heat transfer. In standard smooth pipes, the transition to turbulence typically begins at a Reynolds number of around 2300, but with the turbocollector’s internal geometry, turbulence is initiated at approximately Re = 1800.
Model development
Below, we will outline how the mathematical model for the turbocollector was developed — with minimal use of mathematics. First, we introduce the concept of Computational Fluid Dynamics (CFD) and the challenges involved in modelling turbulent flow. We then turn to the simulation results presented in the work of Hidman N. (2025), and explore what his findings reveal about the effective borehole thermal resistance and pressure drop associated with the turbocollector.
!Note
The model described below is based on the work of Hidman N. (2025). While his original paper delves far deeper into the mathematical and numerical details of the simulations and correlation development, the goal of this article is to provide a high-level understanding of how the model was constructed. For those interested in the full details, the original publication is available here.
What is CFD?
CFD stands for Computational Fluid Dynamics and is one of the most important fields in engineering today. It is used to simulate fluid behaviour in chemical plants, optimise the shape of aircraft wings to maximise lift, assess the aerodynamic performance of vehicles, predict wind turbine output, and much more. When it comes to modelling the thermohydraulic behaviour of the turbocollector, CFD is the go-to method.
Modelling turbulence
Although CFD simulations are widely used, accurately modelling turbulence remains extremely challenging. Turbulence (as discussed earlier in the article on the Reynolds number, which you can find here) is a highly chaotic state of fluid motion for which no analytical solution exists. This is because turbulence occurs across a range of both temporal and spatial scales. For instance, when an aeroplane flies through a cloud, you might observe large-scale vortices — and within those, even smaller swirling structures, and so on. To fully capture this turbulent behaviour, simulations must resolve down to the finest resolution.
In literature, three main models are commonly used to simulate turbulence — all of which are illustrated below:
- RANS (Reynolds-Averaged Navier-Stokes) is the fastest but least accurate approach. As shown in the figure, the fine-scale vortices are completely smoothed out, making this method unsuitable for modelling the turbocollector.
- LES (Large Eddy Simulation) is a more advanced method that distinguishes between large-scale and small-scale turbulence. The larger eddies are resolved directly, while smaller-scale turbulence is modelled. This approach offers better fidelity, as some flow structures become visible.
- DNS (Direct Numerical Simulation) is the most accurate — but also the most computationally intensive — method, as it solves the fluid equations numerically across extremely small time and space intervals. The figure clearly shows that this method provides the most detailed and realistic representation of turbulence.
In order to simulate the fins inside the pipe with high accuracy, a Direct Numerical Simulation (DNS) was performed.
!Note
All fluids — whether water, air, or others — are governed by the Navier–Stokes equations. Since their formulation, no one has been able to find a general analytical solution to them. This is why we must rely on computationally intensive numerical methods such as DNS. The importance of this problem is so significant in physics that a one-million-dollar prize has been offered to anyone who can solve it. You can find more information on this challenge here.
Simulation results
Niklas Hidman (2025) simulated both a smooth pipe and a turbocollector pipe using DNS. The results for the smooth pipe, which serve more as a reference scenario (or a model check), are shown below.
Every simulation started with a Reynolds number of 3300 in order to ensure a turbulent/transient flow. Afterwards, the flow rate was lowered in multiple steps until a laminar regime was reached. In the figure above, one can clearly see that the smooth pipe for Re = 3300 has a homogeneous colour, indicating a good mixing from the turbulence. The small red regions at the edge are some boundary effects where the flow is laminar.
When the flow is at Re = 2025, the figure is totally different. Here, one can clearly see a temperature difference between the inner and outer fluid layers, indicating a clear laminar flow behaviour. This is in line with what we already knew for smooth pipes.
The figure below shows the same simulation for the turbocollector. The story is the same for Re = 3300, where the flow is also turbulent, just as with the smooth pipe. When the flow rate is reduced (and hence also the Reynolds number), the flow stays rather well mixed. It is only at around Re < 1800 that a solid boundary layer starts forming, which is why Hidman N. (2025) concluded that the transient zone starts at Re = 1800, which is significantly before the smooth pipe transition region.
Given the simulation results above, the graphs below can be constructed for both the friction factor and the Nusselt number.
!Note
The friction factor is used for the calculation of the pressure drop (as we discussed previously here), where a higher friction factor gives a larger pressure drop. The Nusselt number is a dimensionless number that is the ratio between the convective and conductive heat transfer rate of the fluid. To put it simply, a higher Nusselt number gives a better heat transfer to the pipe and hence a lower effective borehole thermal resistance (as we discussed here).
For the friction factor, we have both the analytical solution for the laminar flow in a smooth pipe (the dotted blue line) and the correlation for the turbulent flow (in green). You can see that the simulated smooth pipe (noted as ‘Smooth DNS’) follows the laminar friction factor, whereas the turbocollector (noted as ‘Alternating DNS’) deviates at around Re = 1800, due to the fact that the flow becomes transient.
For the Nusselt number, we have the line with the laminar solution, which is constant. At around Re = 3000, the Gnielinski correlation can be used to calculate the Nusselt number for the turbulent flow. In between, typically, an interpolation is made for the smooth pipe.
One can see that the turbocollector (indicated with diamonds) deviates from the smooth-laminar solution at around Re = 1800, indicating a better heat transfer. Around Re = 2300, the smooth and turbocollector solution coincide again.
!Note
Note that for the Nusselt number, multiple simulations were done with different Prandtl numbers. A detailed explanation of the Prandtl number is out of scope for this article, but it varies for geothermal applications typically between 20 and 75, depending on the fluid properties (e.g. type of antifreeze) and fluid temperature.
The results above are for the raw physical numbers, which are used for the calculation of the effective borehole thermal resistance and pressure drop. Both of which are discussed below.
!Note
Hidman N. (2025) also developed correlations for both the friction factor and the Nusselt number, which are used for the implementation in GHEtool. The reader is referred to the original paper for more information.
Effective borehole thermal resistance
The graph below shows the effective borehole thermal resistance for a fluid with 25 v/v% MPG at 5°C for both smooth and turbocollector pipes. If we start with the double U-tubes, it is clear that in the laminar regime (<0.2 l/s) both pipes perform more or less the same, with a slight benefit for the turbocollector. The major difference occurs when the turbocollector becomes turbulent at around 0.21 l/s, whereas the smooth pipe remains in a laminar regime until 0.3 l/s, after which the resistance also drops off significantly.
This effect can be explained by the fact that the Nusselt number increases at around Re = 1800 for the turbocollector, whereas it stays constant for the smooth pipe.
The same behaviour is visible for the single pipe, where the same effect appears but at a lower flow rate (which is to be expected, since now 100% of the flow passes through a single pipe). Here, the range of flow rates where the turbocollector performs better than the smooth pipe is smaller.
The location and size of the ‘window’ where the turbocollector behaves better than a regular smooth pipe, depends on quite a lot of parameters like type and percentage of antifreeze and fluid temperatures. Since GHEtool works with variable fluid properties (as was explained in this article), one can also expect sometimes different behavior during heating and cooling, since the Reynolds number changes over time. The figure below shows the effective borehole thermal resistance when using of MPG 25 v/v% instead o MEG. Due to the overall higher viscosity, the transition to a transient flow is shifted to higher flow rates.
Pressure drop
Besides the borehole resistance, the pressure drop is also important. Below you can see the results for the same fluid.
Looking at the graph, it is clear that the turbocollector has similar pressure drop characteristics as the smooth pipe, except in the transition zone (for the single U at around 1.2 l/s and for the double one at around 2.5 l/s). This is due to the earlier start of the transient regime, which causes an increase in the friction factor and hence also in the pressure drop.
It might seem strange at first that putting fins inside a pipe causes only a slight increase in the overall pressure drop. The explanation is given by another result from the work of (Hidman N., 2025).
You can see that for a larger fin height (where a height of 0 is equivalent to a smooth pipe), the Nusselt number increases. This is easy to understand since bigger fins will have more effect as a turbulator. The downside of higher fins is also that the friction factor increases significantly after a fin height of around 0.6 mm. Therefore, the turbocollector design uses small fins — enough to induce turbulence, but at the same time limit the pressure drop.
!Note
From a physics point of view, it’s not so much the fin height itself that’s important, but the ratio of the fin height to the pipe diameter. It was checked that for all different turbocollector pipes, this ratio is between 0.015–0.025, corresponding to a fin height of 0.6 to 1.2 mm in the figure above.
Turbocollector in GHEtool
To implement the Turbocollector in GHEtool, some changes were made to the interface. From now on, the different pipe options are available in a searchable drop-down list, where we have added some generic smooth pipes alongside the Separatus probe and now also the Turbocollector. The fluid regime (laminar or transient) is also updated according to the selected pipe.
Conclusion
This article discussed in detail the mathematical modelling of the Turbocollector, based on the recent work of Hidman N. (2025). It was shown that the clockwise and counterclockwise rotating fin design creates a transient flow starting at around Re=1800, whereas the transition to a turbulent flow in a smooth pipe starts only at around Re=2300. The friction factor is higher for the Turbocollector in the range 1800 < Re < 2300 due to the induced turbulence, but it converges towards the smooth pipe solution in both the laminar and fully turbulent regimes.
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