The influence of borehole lengths on a numerical model of a double-tube vertical ground heat exchanger

GHEs are underground pipes that transmit heat between the earth and pipes. ANSYS Fluent was used to numerically investigate the thermal and hydraulic performance of a vertical twin tube ground-linked heat exchanger in a pile foundation in cooling mode. The CFD analysis uses three borehole length models—M1-10 m, M2-15 m, and M3-20 m—with flow rates from 1-100 lit/min and Reynolds numbers from 162 to 1625. The numerical results show that the average heat transfer rate of the Model M1 was 13% higher than that of the Model M2, 32% higher than that of the Model M3, and 95% higher than that of the Model M2. The pressure drop was minimal for 1 to 5 lit/min (laminar flow condition) but very high for 10 to 100 lit/min. The bore cavity length increased the pressure drop and decreased the average output temperature. These two-tube vertical GHEs with optimized length and selection of pipe materials can improve natural convection heat transfer by contacting ground waters.


Introduction
Ground pair heat exchangers in pile foundations exchange heat with concrete and underground soil [1].Winter and summer soil temperatures are similar.Winter soil temperatures are higher than summer soil temperatures.A ground-coupled heat exchanger dissipates summer heat and extracts winter heat.Heat pumps use motor energy to generate heat [2].Ground source heat pump (GSHP) systems are more efficient and eco-friendlier.GCHE is used for HVAC, cooling ice, industrial usage, agricultural drying, greenhouse heating, space heating, aquaculture ponds, and raceway heating, and more [3].The ground temperature is almost stable after a certain depth.GCHEs are subterranean pipes.Horizontal trenches or vertical boreholes can bury the heat exchanger.It's installed underground.GCHPs use the environment to provide clean, efficient, and energy-saving heating and cooling year-round.3D vertical GCHE model analysis [4].Geothermal down-hole heat exchanger analysis using a new numerical approach.This model aids low-enthalpy geothermal reservoir utilization [5].A geothermal heat exchanger was tested under coupled heat conduction and groundwater advection [6].Numerical and simulation models were constructed [7][8][9].GCHE performance and economic installation depend on environmental and mechanical parameters such as soil temperature and qualities, pressure drop, flow rate, length, and heat exchanger diameter [10].However, considering cost-and time-intensive practical applications, the heat transfer and pressure drop within twin tube vertical GHE in terms of borehole lengths should be explored more numerically.This study deals with the influence of borehole lengths on the thermal and hydraulic performance of twin tube vertical ground heat exchangers in pile foundations.The lack of literature on borehole length-based thermal and hydraulic performance in geothermal systems has inspired the study.Performance evaluation based on ideal borehole lengths, pressure drop, and heat transfer characteristics are the article's contributions.We use ANSYS Fluent to estimate heat transfer enhancement and pressure drop in three double tubes vertical GHE borehole length models: M1 (10m), M2 (15m), and M3 (20m).The numerical results show that the average heat transfer rate of Model M1 was 13% higher than that of the Model M2, 32% higher than that of the Model M3, and 95% higher than that of the Model M2.The pressure drop was minimal for 1 to 5 lit/min (laminar flow condition) but very high for 10 to 100 lit/min.This investigation shows twin tube vertical GHE thermofluidic performance.Heat transfer and pressure decrease are critical.These parameters show how well heat is transported between the earth and the system's fluid.Studying heat transfer and pressure drop optimizes the twotube vertical ground heat exchanger.By testing borehole lengths, you can find the best one for heat transfer and pressure drop.This understanding helps develop cost-effective geothermal systems.Higher heat transfer rates and lower pressure drops improve system performance and energy usage.Analyzing these aspects can help you improve energy efficiency for sustainable and ecologically friendly applications.Understanding heat transfer and pressure drop helps choose system size, fluid flow, and rate equipment.Consider these criteria to optimize the heat exchanger system and avoid pressure drop and heat transfer difficulties.In conclusion, investigating heat transfer and pressure drop in this paper is vital for evaluating system performance, optimizing design, improving energy efficiency, and making practical judgments about the double tube vertical ground heat exchanger in a pile foundation.

Configuration of Physical Model
Double-tube vertical heat exchangers have intake and exit tubes.Concrete conducts heat better than earth.The outside pipe should withstand underground pressure.Outer pipe thermal conductivity should be high, and inner pipe should be low.Since concrete conducts heat better than the earth, pile foundations may transfer heat well.Figure 1 depicts an axisymmetric view of a ground-coupled double-tube heat exchanger in pile foundation and soil layer pile foundation and soil heat exchanger.The center line of the tubes of a double-tube heat exchanger is the point of symmetry.Thus, for numerical analysis purposes, a 3D model can be reduced to a 2D axis-symmetric issue.As a result, we'll be able to devote less time to analysis, and even larger models won't be too much trouble.The model's symmetry axis is depicted in Figure 2. Pipe length will be simulated to change while Inlet and Outlet pipe diameters remain constant.The model's dimensions are shown in Table 1.

Theory
To analyze the vertical GCHE, numerical simulations were carried out by using the commercial CFD software ANSYS FLUENT 18. 1 [21].The governing equation is given below [22]: For 2D axisymmetric geometries, the continuity equation is given by Where p is density, t is time, x is axial coordinate, r is radial coordinate, Vx is axial velocity and Vr is radial velocity.The axial and radial momentum conservation equations of 2D axisymmetric geometries are given by Eq. ( 2) and ( 3) Where  is viscosity, P is pressure and The energy equation is given by Where h is enthalpy,   is turbulence viscosity, and   is constant.
In the ground soil region, the energy transport equation given by Where,   is density of soil, Cp is the specific heat of soil, k is the thermal conductivity of soil and T is temperature.

Heat Transfer Rate
Heat transfer rates were calculated to investigate the thermal performance of the GHEs.The heat transfer rate can be calculated by the following: where m is the mass flow rate (kg/s), Cp is the specific heat (J/kg K), and ∆T is the temperature difference between the inlet and outlet of circulated water (K).Then heat transfer rate per meter borehole depth is defined as follows: where L is the length of the borehole.
Evaluating the average heat transfer rate over 24 hours using 10m, 15m, and 20m boreholes as criterion.

Pressure Drop
To verify the pressure, drop through GHE tubes due to water flow, the pressure drop is also calculated by using the following equations: where ∆P is the pressure drop (Pa), fs is the friction factor, L is the tube length (m), D H is the hydraulic diameter of the tube (m), ρ is the density of the fluid (kg/m3), V is the fluid velocity (m/s).
For a straight tube, the friction factor can be calculated by Hagen-Poiseuille equation for laminar flow and by Blasius equation for turbulent flow Also, pressure drop caused by sudden contraction when water enters in outlet tube from the inlet tube can be calculated by: where Vo is the velocity in the outlet tube and Vi is the velocity in the inlet tube.Then the total pressure drop through the GHE is calculated by

Axisymmetric model
In this analysis, ANSYS FLUENT has been used.First, the axisymmetric model is designed by the Design Modeler (DM).

Mesh generation
To achieve precise results, it is crucial to handle meshing correctly.We employed appropriate meshing techniques to obtain the desired outcome.We applied extensive smoothing, ensuring the central area was refined accordingly.Additionally, we utilized the face split function to achieve a more accurate mesh.To reduce the overall number of meshes while maintaining accuracy, we used the bios mesh tool to increase mesh density specifically around and inside the GCHE tubes while the mesh size was increased distant from the GHE tube.The densified region is depicted in Fig. 3.The launcher's Fluent configuration was upgraded to higher precision.The axisymmetric solver, transient time step, and pressure-based, absolute velocity formulation have all been implemented.The impact of gravity on acceleration is also considered.The problem is solved using the energy equation and the K-epsilon, general, scalable wall function model.In the inlet region, we employ a boundary condition of velocity inlet, and in the outlet region, we use a boundary condition of constant pressure-outlet.The working pressure has been set to 1 atm, and the temperature has been set to 293.15K.The interface walls were then connected, and convergence requirements of 10-6 residuals were established.For a 24-hour computation after initialization, a time step size of 30 and a total of 2880 time steps are taken into account.

Boundary Condition
A wide range of flow rates from 1 lit/min to 100 lit/min were all considered for the intake water flow rate, while the inlet water temperature was fixed at 308.15 degrees Celsius.The upper surface was maintained at a constant uniform temperature of 293.15K.No heat flux was considered at the side wall from the center line, and a heat flux of 65 / 2 was applied to the bottom surface [11].
The ground temperature on November 28, 2017, at the Khulna University of Engineering and Technology, was determined using the Kasuda equation [12].
The following correlation best describes Kasuda [12]'s findings regarding the relationship between seasonality and subsurface temperature: Where: T = Temperature T mean = Mean surface temperature (average air temperature) T amp = Amplitude of surface temperature (maximum air temperature minus minimum air temperature) Z = Depth below the surface, α = Thermal diffusivity of the ground (soil)   = current time (day),  ℎ = day of the year of the minimum surface temperature To apply the above equation weather variables are taken from MSN Weather.

Mesh Element Independence Test
A flow rate of 1 l/min and an input temperature of 308.15K is required for the mesh element independence test.Despite adding more components, the outlet temperature hardly shifts.There were 142800 elements chosen for the M-1 model, 205200 for the M-2 model, and 356850 for the M-3 model.The average outlet temperature increased with the increases in borehole length.For example, the Average outlet temperature was 302.96K, 301.85 K, and 301.34K for 1 lit/min flow rate respectively model M-1(10m), M-2(15m), M-3(20m).

Model Validation
The experimental result used to verify the M-3 model in the present work was [11].In addition, numerical results support the M-3 model [10].
The following table details the thermo-physical parameters of the materials and the testing conditions used by Saga University.The soil is clay up to 10 meters, and sandy clay below that.The thermosphysical attributes are displayed in Table 4. Figure 5 shows how the current simulation's average heat transfer rate stacks up against that of experimental and numerical simulations.The present result confirms that experimental and numerical analysis follows the same pattern.Similarly, the current investigation likewise yields promising results.Heat transfer increases as the output temperature decreases.Heat transmission increases in Fig. 6 as the temperature difference between the intake and output rises.Longer boreholes result in cooler temperatures at the outflow.Increasing the flow reduces the temperature gradient.Up to a flow rate of 5 lit/min, heat transfer is greatest for borehole lengths of 10 meters, compared to 15 meters and 20 meters.The borehole's length, in addition to the incoming and outgoing velocities, determines the pressure drop.How big the inlet and output tubes are, will determine the answer.However, the diameters of the tubes at the inlet and outflow are set.Since the diameter of the outlet pipe was less than that of the inlet tube, the inlet velocity was less than the outlet velocity.As a result of the rapid reduction in diameter, the flow entering the exit tube picked up speed.As flow rates increase, so does the amount of pressure drop.From 1 to 10 l/min, the pressure drop is moderate, but between 10 and 40 l/min, it becomes significant.The longer the borehole is, the more pressure is lost.Up to 10 l/min, there is only a small difference in pressure drop across the three models (Fig. 8), but after that, the pressure drop grows exponentially with borehole length.As borehole length increases, there is a corresponding increase in pressure drop.This is primarily due to two factors: frictional losses along the length of the borehole and an uneven velocity distribution inside the borehole.Frictional losses occur because the longer borehole has a larger surface area in contact with the flowing fluid, due to the viscosity of the fluid and frictional coefficient of the pipe material resulting in increased fluidic resistance and higher pressure drop.Additionally, the uneven velocity distribution leads to variations in pressure along the borehole, contributing to an overall increase in pressure drop.Considering this relationship is crucial for balancing borehole length and system efficiency, as longer boreholes can lead to higher pressure drops and potentially reduce the overall efficiency of the heat exchanger system.To explain the results, smaller borehole radii demonstrate higher rates of heat transfer compared to larger radii.This is primarily due to the increased contact surface area between the fluid and the surrounding ground in smaller boreholes.Additionally, smaller borehole radii promote a steeper temperature gradient, which facilitates a greater temperature difference and enhances the rate of heat transfer.However, it is important to strike a balance between achieving optimal heat transfer and considering practical constraints such as fluid flow restrictions and pressure drops, as extremely small radii may not be feasible.Therefore, Understanding the behavior of borehole length, radius, pressure drop, and heat transfer is important in optimizing the design and operation of double-tube vertical ground heat exchangers in pile foundations.

Conclusion
The cost of pumping rises rapidly as the difference in pressure between the intake and exit grows.The pressure drop is quite high from 1 to 10 liters per minute, but it increases to a significant level between 10 and 40 liters per minute.When the pressure drop is high, it takes more energy to pump the same amount of fluid.Therefore, a flow rate in the range of 10 l/min to 40 l/min should not be selected.Laminar flow describes velocities between 1 and 10 l/min, while turbulent velocities exceed 15 l/min.Costs rise with a rise in turbulence.Accordingly, we expect the flow zone to be laminar.Heat transfer is adequate, and pressure drop is tolerable, with a flow rate of 2-5 liters/min.A flow rate between 2 and 5 liters per minute is optimal, depending on the application.

Figure 2 :
Figure 2: Two-dimensional with concrete& and soil layer and its symmetric axis

Figure 7 :
Figure 7: Average heat transfer per meter (W/m) with the flow rate (lit/min)

Figure 8 :
Figure 8: Pressure drop (Pa) with flow rate

Table 2 :
Materials thermo-physical properties used in the numerical model.

Table 3 :
Different parts dimensions of the axisymmetric model

Table 4 :
[10]rials thermos-physical properties used to validate the model M-3[10]The outlet temperatures of the M-3 model for the current simulation and the previous one byAliet al.16 after 24 hours of operation at a flow rate of 2 l/min are, respectively, 295.85 k and 295.64 k.Further findings are detailed below.