Skip to content

Commit

Permalink
Merge branch 'web-img-shortcut' into 'master'
Browse files Browse the repository at this point in the history
[web] Removed img shortcut in favour of Hugo's figure

See merge request ogs/ogs!4775
  • Loading branch information
endJunction committed Oct 26, 2023
2 parents a5b428f + 437c849 commit c6720e6
Show file tree
Hide file tree
Showing 79 changed files with 251 additions and 279 deletions.
5 changes: 3 additions & 2 deletions web/assets/css/main.css
Original file line number Diff line number Diff line change
Expand Up @@ -139,9 +139,10 @@ body {
counter-reset: figcaption;
}

figcaption::before {
figcaption p::before,
figcaption h4::before {
counter-increment: figcaption;
content: "Fig. "counter(figcaption) ": "
content: "Fig. " counter(figcaption) ": "
}

figcaption {
Expand Down
Original file line number Diff line number Diff line change
Expand Up @@ -14,4 +14,4 @@ We present the drainage of an excavation benchmark in [this PDF](/docs/benchmark

Here's an impression of the problem and its results:

{{< img src="drainage_excavation.png" >}}
{{< figure src="drainage_excavation.png" >}}
Original file line number Diff line number Diff line change
Expand Up @@ -100,11 +100,11 @@ info: OGS terminated on 2018-10-12 06:30:13+020

The numerical solution shown in the following picture is almost a linear
gradient:
{{< img src="square_1e2_volumetricsourceterm_pcs_0_ts_1_t_1.000000_Pressure_VolumetricSourceTerm.png" >}}
{{< figure src="square_1e2_volumetricsourceterm_pcs_0_ts_1_t_1.000000_Pressure_VolumetricSourceTerm.png" >}}
The line plot along the $x$ axis shows that the solution is a quadratic
function and is in very good agreement to the analytical solution:
{{< img src="square_1e2_volumetricsourceterm_pcs_0_ts_1_t_1.000000_Pressure_AnalyticalSolution_VolumetricSourceTerm.png" >}}
{{< figure src="square_1e2_volumetricsourceterm_pcs_0_ts_1_t_1.000000_Pressure_AnalyticalSolution_VolumetricSourceTerm.png" >}}

The difference between the computed solution and the analytical solution is in
the range of machine precision and therefore almost negligible:
{{< img src="square_1e2_volumetricsourceterm_pcs_0_ts_1_t_1.000000_diff_Pressure_AnalyticalSolution_VolumetricSourceTerm.png" >}}
{{< figure src="square_1e2_volumetricsourceterm_pcs_0_ts_1_t_1.000000_diff_Pressure_AnalyticalSolution_VolumetricSourceTerm.png" >}}
Original file line number Diff line number Diff line change
Expand Up @@ -123,12 +123,12 @@ A last major part of the output was produced by the linear equation solver (LIS

Compared to the analytical solution presented above the results are very good but in a single point:

{{< img src="square_1e2_neumann_abs_err.png" >}}
{{< figure src="square_1e2_neumann_abs_err.png" >}}

Both Dirichlet boundary conditions are satisfied.
The values of gradients in x direction along the right side and y directions along the top sides of the domain a shown below:

{{< img src="square_1e2_neumann_gradients.png" >}}
{{< figure src="square_1e2_neumann_gradients.png" >}}

The homogeneous Neumann boundary condition on the top side is satisfied (ScalarGradient_Y is close to zero).
The inhomogeneous Neumann boundary condition on the bottom is satisfied only for $y > 0.3$ (where the ScalarGradient_X is close to one) because of incompatible boundary conditions imposed on the bottom right corner of the domain.
Original file line number Diff line number Diff line change
Expand Up @@ -67,8 +67,8 @@ It will produce some output and write the computed result into a data array of t

### Comparison of the analytical solution and the computed solution

{{< img src="circle_1e6_gwf_with_nodal_source_term_analytical_solution_head.png" >}}
{{< figure src="circle_1e6_gwf_with_nodal_source_term_analytical_solution_head.png" >}}

{{< img src="circle_1e6_gwf_with_nodal_source_term_diff_analytical_solution_head.png" >}}
{{< figure src="circle_1e6_gwf_with_nodal_source_term_diff_analytical_solution_head.png" >}}

{{< img src="circle_1e6_gwf_with_nodal_source_term_diff_analytical_solution_head_log_scale.png" >}}
{{< figure src="circle_1e6_gwf_with_nodal_source_term_diff_analytical_solution_head_log_scale.png" >}}
Original file line number Diff line number Diff line change
Expand Up @@ -104,7 +104,7 @@ The left figure shows the pressure along the line, in the right figure the
difference between the analytical solution and the numerical calculated solution
is plotted.

{{< img src="line_1e1_robin_left.png" >}}
{{< figure src="line_1e1_robin_left.png" >}}

## Second benchmark: Problem specification and analytical solution

Expand Down
Original file line number Diff line number Diff line change
Expand Up @@ -181,15 +181,15 @@ info: OGS terminated on 2018-10-10 09:22:17+020

### Comparison of the numerical and analytical solutions

{{< img src="square_1e3_poisson_sin_x_sin_y_sourceterm_Pressure_PythonSourceTerm.png" >}}
{{< figure src="square_1e3_poisson_sin_x_sin_y_sourceterm_Pressure_PythonSourceTerm.png" >}}
The above picture shows the numerical result. The solution conforms in the edges
to the prescribed boundary conditions.
{{< img src="square_1e3_poisson_sin_x_sin_y_sourceterm_Diff_Pressure_AnalyticalSolution_PythonSourceTerm.png" >}}
{{< figure src="square_1e3_poisson_sin_x_sin_y_sourceterm_Diff_Pressure_AnalyticalSolution_PythonSourceTerm.png" >}}
Since a coarse mesh ($32 \times 32$ elements) is used for the simulation the
difference between the numerical and the analytical solution is relatively large.

#### Comparison for higher resolution mesh ($316 \times 316$ elements)

{{< img src="square_1e5_poisson_sin_x_sin_y_sourceterm_Diff_Pressure_AnalyticalSolution_PythonSourceTerm.png" >}}
{{< figure src="square_1e5_poisson_sin_x_sin_y_sourceterm_Diff_Pressure_AnalyticalSolution_PythonSourceTerm.png" >}}
The difference between the numerical and the analytical solution is much smaller
than in the coarse mesh case.
Original file line number Diff line number Diff line change
Expand Up @@ -34,7 +34,7 @@ For this benchmark, Two different scenarios were carried out by applying two dif

The detailed input parameters can be seen from the 3D_2U_BHE.prj file. The inflow temperature of the BHE, which was imposed as boundary condition of the BHE is shown in Figure 1. All the initial temperatures are set as 22 $^{\circ}$C. The flow rate within each U-pipe is set to $2.0\times10^{-4}$ $\mathrm{m^{3} s^{-1}}$ during the whole simulation time.

{{< img src="In_out_temperature_comparison.png" width="200">}}
{{< figure src="In_out_temperature_comparison.png" >}}

Figure 1: Inflow temperature curve and outflow temperature comparison

Expand All @@ -58,7 +58,7 @@ The computed results from scenario by adopting the fixed inflow boundary conditi
The OGS numerical outflow temperature over time was compared against results of the FEFLOW software as shown in the Figure 1. And the vertical distributed temperature of circulating water was presented in Figure 2 after operation for 3300 s.
The comparison figures demonstrate that the OGS numerical results and FEFLOW results can match very well and the biggest absolute error of outflow temperature is 0.20 $^{\circ}$C after 360 s' operation, while such error decreases to 0.037 $^{\circ}$C after 3600 s' operation. The maximum relative error of vertical temperature is 0.019 \% after operation for 3300 s.

{{< img src="vertical_temperature_distribution.png" width="200">}}
{{< figure src="vertical_temperature_distribution.png" >}}

Figure 2: Comparison of vertical temperature distribution from scenario by adopting the fixed inflow boundary condition

Expand All @@ -71,7 +71,7 @@ Besides, by setting python bindings, the current OGS `Heat_Transport_BHE` proces
In this way, the computed vertical distributed circulating fluid temperature is updated to the black and red solid line illustrated in the figure 3.
It shows that in this case, the difference between the OGS and FEFLOW models is becoming much closer to each other, which is about 0.037 $^{\circ}$C.

{{< img src="vertical_temperature_distribution_powerBC.png" width="200">}}
{{< figure src="vertical_temperature_distribution_powerBC.png" >}}

Figure 3: Comparison of vertical temperature distribution from scenarios by adopting the power boundary conditions

Expand Down
Original file line number Diff line number Diff line change
Expand Up @@ -63,7 +63,7 @@ The TESPy version 0.3.2 is used in this benchmark.

Two different pipe network setup were constructed for this benchmark.

* A one-way pipe network (see Figure 1a)
#### A one-way pipe network (see Figure 1)

In this setup, the refrigerant mass flow rate is given in $kg/s$, as this is the default setting in the TESPy model (see `./pre/3bhes.py`).
After being lifted by the pump, the refrigerant inflow will be divided into 3 branches by the splitter and then flow into each BHEs.
Expand All @@ -76,57 +76,43 @@ During the calculation of the TESPy solver, the flow density and the related spe
To check their concrete value under specific temperature and pressure conditions, interested readers may refer to e.g. the 'PropsSI' function introduced in the webpage of CoolProp.
For the fast execution of this benchmark, the total simulation time is shorten to 600 seconds. If the reader wishes to reproduce the same results, a full simulation of 6 months needs to be performed.

{{< img src="BHE_network.png" width="200">}}
{{< figure src="BHE_network.png" caption="One-way pipeline network model" >}}

Figure 1a: One-way pipeline network model

* A closed-loop pipe network (see Figure 1b)
#### A closed-loop pipe network (see Figure 2)

The setup for a closed-loop network model is illustrated in Figure 1b.
Compared to the configuration in the one-way network, the refrigerant in the closed loop network is circulating through the entire system.
In this case, the flow rate will be automatically adjusted by the water pump in each time step, as its pressure head is directly linked to the flow rate. Subsequently, the flow rate is determined by the pressure losses in the BHE array.

{{< img src="BHE_network_closedloop.png" width="200">}}

Figure 1b: Closed-loop pipeline network model
{{< figure src="BHE_network_closedloop.png" caption="Closed-loop pipeline network model" >}}

## Results

The evolution of the soil temperature at 1 m distance away from the 3 BHEs are shown in Figure 2.
The evolution of the soil temperature at 1 m distance away from the 3 BHEs are shown in Figure 3.
Compared with the BHE \#1 and BHE \#3, the soil temperature near the BHE located at the centre (BHE \#2) shows a deeper draw-down.
It indicates that a thermal imbalance is occurring in the center of the BHE array.
This imbalance leads to a lower outflow temperature from the BHE \#2, which is shown in Figure 3.
Figure 4 depicts the evolution of the heat extraction rate of each BHE over the time.
This imbalance leads to a lower outflow temperature from the BHE \#2, which is shown in Figure 4.
Figure 5 depicts the evolution of the heat extraction rate of each BHE over the time.
Compared to the decrease of the heat extraction rate on the centre BHE \#2, the rates on the other two BHEs located at the out sides was gradually increasing.
It indicates that the heat extraction rate is shifting from the centre BHE towards the outer BHEs over the heating season.
In this figure, the difference between the total heat extraction rate of all BHEs and the preset 3750 $W$ imposed on the heat pump is due to the hydraulic loss within each pipe in the pipe network.

In comparison to the one-way setup, the closed-loop network shows a slightly different behaviour.
The evolution of inflow refrigerant temperature and flow rate entering the BHE array is shown in Figure 5.
The evolution of inflow refrigerant temperature and flow rate entering the BHE array is shown in Figure 6.
With the decreasing of the working fluid temperature over the time, the system flow rate decreases gradually.
Figure 6 depicts the thermal load shifting phenomenon with the closed-loop model.
Figure 7 depicts the thermal load shifting phenomenon with the closed-loop model.
Except for the thermal shifting behavior among the BHEs, the averaged heat extraction rate of all BHEs (black line) increases slightly over the time.
This is due to the fact that additional energy is required to compensate the hydraulic loss of the pipe.

{{< img src="Soil_temperature.png" width="200">}}

Figure 2: Evolution of the soil temperature located at the 1 m distance away from each BHE

{{< img src="Inflow_and_outflow_temperature.png" width="200">}}

Figure 3: Evolution of the inflow and outflow refrigerant temperature of each BHE

{{< img src="Heat_extraction_rate.png" width="200">}}

Figure 4: Evolution of the heat extraction rate of each BHE
{{< figure src="Soil_temperature.png" caption="Evolution of the soil temperature located at the 1 m distance away from each BHE" >}}

{{< img src="Inflow_temperature_and_flow_rate.png" width="200">}}
{{< figure src="Inflow_and_outflow_temperature.png" caption="Evolution of the inflow and outflow refrigerant temperature of each BHE" >}}

Figure 5: Evolution of the inflow refrigerant temperature and flow rate entering the BHE array
{{< figure src="Heat_extraction_rate.png" caption="Evolution of the heat extraction rate of each BHE">}}

{{< img src="Heat_extraction_rate_closedloop.png" width="200">}}
{{< figure src="Inflow_temperature_and_flow_rate.png" caption="Evolution of the inflow refrigerant temperature and flow rate entering the BHE array" >}}

Figure 6: Evolution of the heat extraction rate of each BHE with close loop network model
{{< figure src="Heat_extraction_rate_closedloop.png" caption="Evolution of the heat extraction rate of each BHE with close loop network model" >}}

## References

Expand Down
Original file line number Diff line number Diff line change
Expand Up @@ -72,9 +72,7 @@ The BHE parameters are only relevant for the numerical model and are adopted
from the [3D Beier sandbox
benchmark]({{< ref "3D_Beier_sandbox.md" >}}).

{{< img src="mesh.png" width="150">}}

Figure 1: Geometry and mesh of the BHE model
{{< figure src="mesh.png" caption="Geometry and mesh of the BHE model">}}

## Results

Expand All @@ -86,14 +84,9 @@ and analytical solution match very well as the maximum relative error of
ground temperature is less than 0.2 \%. The largest difference is found near
the BHE node towards which the analytical solution approaches infinity.

{{< img src="temperature_soil_2years.png" width="150">}}

Figure 2: Ground temperature distribution after two years at $z=-7$ m.

{{< img src="rel_err.png" width="150">}}
{{< figure src="temperature_soil_2years.png" caption="Ground temperature distribution after two years at $z=-7$ m.">}}

Figure 3: Comparison of OGS-6 results and analytical solution. Note the
singularity of the analytical solution at the BHE node.
{{< figure src="rel_err.png" caption="Comparison of OGS-6 results and analytical solution. Note the singularity of the analytical solution at the BHE node.">}}

## References

Expand Down
Original file line number Diff line number Diff line change
Expand Up @@ -30,31 +30,23 @@ The numerical model was established using dual continuum method Diersch et al. (
| Grout thermal conductivity | $\lambda_{g}$ | 0.806 | $\mathrm{W m^{-1} K^{-1}}$ |
| Grout heat capacity | $(\rho c)_{grout}$ | $3.8\times10^{6}$ | $\mathrm{Jm^{-3}K^{-1}}$ |

{{< img src="numerical_geometry_of_BHE.png" width="200">}}

Figure 1: Sandbox model
{{< figure src="numerical_geometry_of_BHE.png" caption="Sandbox model">}}

In Beier's experiment, the inner diameter of aluminum pipe is 12.6 $\mathrm{cm}$ and the borehole wall thickness of aluminum is 0.2 $\mathrm{cm}$. In the numerical model, the borehole wall feature cannot be reflected because of the line elements. Therefore, the diameter of the BHE in numerical model was set 13 $\mathrm{cm}$. Meanwhile, the grout's thermal conductivity was increased from original 0.73 $\mathrm{W m^{-1} K^{-1}}$ to 0.806 $\mathrm{W m^{-1} K^{-1}}$. As for the circulating water in the BHE pipe, the thermal physical parameters are taken from the state at an average temperature of approx. 309.15 K.

## OGS-6 Input Files

The detailed input file can be seen from the .prj file. The inflow temperature of the BHE, which was imposed as boundary condition of the BHE can be shown in Figure 2. Initial conditions of inflow and outflow temperature for the BHE were directly obtained from the measurements at t=0. For the initial soil temperature, the average value of all sensors placed in the sand and the borehole wall was set in the numerical model.

{{< img src="Inflow_temp.png" width="200">}}

Figure 2: Inflow temperature curve as the BHE boundary condition
{{< figure src="Inflow_temp.png" caption="Inflow temperature curve as the BHE boundary condition">}}

## Results

The numerical outflow temperature of OGS-5 (Shao et al. (2016)) and OGS-6 was compared with the experimental results, which is presented in the Figure 3. And the soil temperature at different locations among experimental and numerical results were compared and shown in the Figure 4. The comparison figures demonstrate that the numerical results and experimental data can fit very well and the largest relative error is 0.17\% on the wall temperature and 0.014\% on the outflow temperature. The initial temperature of borehole wall in numerical model was set an average value as mentioned in the above, which has initial error of 0.07 K compared to the experimental data. Besides, normally, the error of measuring temperatures during experiment, difference on the real thermal physical parameters of the sand and the BHE are all at the same value range. Therefore, it can be concluded that the numerical model of 1U-type BHE is fully verified.

{{< img src="comparison_with_experiment_data_and_OGS5.png" width="200">}}

Figure 3: Comparison with experiment and OGS-5 results regarding outflow temperature of the BHE

{{< img src="soil_temp_comparison.png" width="200">}}
{{< figure src="comparison_with_experiment_data_and_OGS5.png" caption="Comparison with experiment and OGS-5 results regarding outflow temperature of the BHE">}}

Figure 4: Comparison of modelled and measured wall and soil temperatures
{{< figure src="soil_temp_comparison.png" caption="Comparison of modelled and measured wall and soil temperatures">}}

## References

Expand Down
Loading

0 comments on commit c6720e6

Please sign in to comment.