DHC Buried Pipes

[bravache]

Update 06/07:

I have added the model PlugFlowDiscretize to address some of the concerns from the previous model, namely: how can we justify a constant temperature boundary condition (constant along the length of the pipe), especially in cases with uninsulated pipes and for long stretch of pipes.

The main change is that this model allows to discretize PlugFlowCore axially. In some ways, this goes against the main benefit of the plug flow model, which is to avoid discretization of the problem, but on the other hand, it allows to more easily justify a semi-fixed temperature boundary for each segment.

I also toyed with the idea of formalizing a "virtual insulation layer" parameter in the model, but it is actually tricky since this layer would take on the soil thermal property, and the pipe is currently not coupled with the soil. This means that if I were to formalize this virtual insulation layer, I would have to also add the soil as a parameter to the PlugFlowDiscretize. In the end, I opted for not adding that option, but showcased how to use virtual insulation in the example DiscretizedBuriedPipes (by simply making the insulation take on the soil conductivity and making the insulation thickness as the virtual layer thickness).

Playing with this PlugFlowDiscretize model in the example confirmed what we suspected: for uninsulated pipes, the number of segment has a significant impact on heat transfer. This impact is not significant for insulated pipes. In the example below, I run 90degC water for 10km, either with no insulation (technically, there is an insulation layer with 100W/mK conductivity) or with 2cm of mineral wool (k=0.035W/mK).

With regard to virtual insulation, the observation is that it can offset the need for discretization to a certain extent. The soil higher conductivity (k=1.58W/mK) does not allow us to fully substitute actual insulation with a layer of soil. In the example below, I run 20degC water for 10km, with either 20cm or 0.2cm of virtual insulation. What we see is that when the pipe is segmented in 10 pieces, the virtual insulation thickness has a moderate impact on the outlet temperature, and when the pipe is not discretized, we see that thicker virtual insulation slightly reduces the gap between 1seg-10seg.

I have tried coming up with an analytical solution for the heat balance between the plug flow pipe model and the ground coupling model which could recommend the right number of segment or virtual insulation thickness, but was not successful. I am open to suggestion though.

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This PR introduces two new models GroundCoupling and UndisturbedSoilTemperature, which are to be used in the modeling of heat transfer of buried pipes found in DHC.

UndisturbedSoilTemperature is a model of the boundary conditions for the prescribed underground temperature. The model relies on information about surface temperature (defined by a sinusoid) and about soil thermal properties, and effectively dampens and shift the sinusoid with increasing depth.

GroundCoupling is a model of heat transfer for a network of coaxial buried pipes. The model relies on the potential flow theory and the mirror image technique, as described in Kusuda (1981), which is the same base model eventually used for single and multiple pipes equations suggested in the ASHRAE District Heating/Cooling Guides.

For each buried pipe (source), a heat sink is virtually created on the other side of the surface, which helps in bounding the heat transfer from the pipe.

For a single pipe, this results in a simple model that is equivalent to the cylindrical radial, steady-state heat transfer equation between the surface of the pipe and the mirror sink. For a multiple pipe network, each pipe transfers heat with other pipes and their sinks.

This model is extensively used in the literature, and should be validated with measurement data, especially for quantifying transient error.

Note: One thing I can't really wrap my head around is that the model equation suggests that the surface temperature (i.e. the mirror isotherm) is equal to the ground reference temperature, but multiple sources suggest to use the undisturbed soil temperature (which is a transformation of the surface temperature) as the reference temperature, even in conjonction with this model. I am unsure how to reconcile those two observations.

[AntoineGautier]

Please see my comments.
A discussion would be useful for me to understand exactly the implication of the steady-state heat transfer computation, and address the ambiguity you mention at #2409 (comment) regarding the ground temperature boundary condition.

[bravache]

I addressed all of the smaller comments, but I still need to work on the assumptions and the validation comment.

[bravache]

@AntoineGautier There are still a few comments that are "unresolved". Take a look and let me know if it's good to go.
Otherwise, I've reversed the changes to the PlugFlowPipe, and pushed them separately in an IBPSA PR. Once that is merged, I will also need to update the example and validation models in this branch, but this can be done in a future PR, and this branch is fully operational regardless of the status if the IBPSA change.

One outstanding change is the proposed structure of the new components. In the end, I've opted to put the new PlugFlowDiscretized directly with the other existing pipe components in the Fluid.FixedResistance library. I also added two new library: Buildings.BoundaryConditions.GroundTemperature and Buildings.Fluid.Geothermal.BuriedPipes, which contain the undisturbed ground temperature module and the ground coupling model respectively. I think this structure makes the most sense, and we can punt the issue of having a dedicated Pipe library for a separate branch.

[bravache]

@mwetter This is ready to be merged.

[mwetter]

This is ready to merge when all tests pass.