Issue31 mixed inlet temperature

CHANGELOG.md

@@ -6,6 +6,7 @@
 
 * [Commit 2bd12bd](https://github.com/MassimoCimmino/pygfunction/commit/2bd12bd254928889431366c2ddd38539e246ef05) - Implemented `UTube.visualize_pipes()` class method.
 * [Issue 30](https://github.com/MassimoCimmino/pygfunction/issues/30) - Laminar regime is now considered for calculation of convection heat transfer coefficient.
+* [Issue 32](https://github.com/MassimoCimmino/pygfunction/issues/32) - g-Functions for bore fields with mixed series and parallel connections between boreholes.
 
 ### Bug fixes
 

doc/source/example_bore_field_thermal_resistance.rst

@@ -0,0 +1,26 @@
+.. examples:
+
+******************************************************
+Calculation of effective bore field thermal resistance
+******************************************************
+
+This example demonstrates the use of the
+:py:func:`.pipes.field_thermal_resistance` function to evaluate the bore field
+thermal resistance. The concept effective bore field thermal is detailed by
+Cimmino [1]_
+
+The following script evaluates the effective bore field thermal resistance
+for fields of 1 to 5 series-connected boreholes with fluid flow rates ranging
+from 0.01 kg/s ti 1.00 kg/s.
+
+The script is located in: 
+`pygfunction/examples/bore_field_thermal_resistance.py`
+
+.. literalinclude:: ../../pygfunction/examples/bore_field_thermal_resistance.py
+   :language: python
+   :linenos:
+
+.. rubric:: References
+.. [1] Cimmino, M. (2018). g-Functions for bore fields with mixed parallel and
+   series connections considering the axial fluid temperature variations.
+   IGSHPA Research Track, Stockholm. In review.

doc/source/example_index.rst

@@ -18,3 +18,5 @@ Examples
    example_equal_inlet_temperature
    example_multiple_independent_Utubes
    example_multipole_temperature
+   example_bore_field_thermal_resistance
+   example_mixed_inlet_conditions

doc/source/example_mixed_inlet_conditions.rst

@@ -0,0 +1,31 @@
+.. examples:
+
+*********************************************************************
+Calculation of g-functions with mixed parallel and series connections
+*********************************************************************
+
+This example demonstrates the use of the :doc:`g-function <gfunction>` module
+and the :doc:`pipes <pipes>` module to calculate *g*-functions considering the
+piping connections between the boreholes, based on the method of Cimmino [1]_.
+For boreholes connected in series, it is considered the outlet fluid temperature
+of the upstream borehole is equal to the inlet fluid temperature of the
+downstream borehole. The total rate of heat extraction in the bore field is
+constant.
+
+The following script generates the *g*-functions of a field of 5 equally spaced
+borehole on a straight line and connected in series. The boreholes have
+different lengths. The *g*-function considering piping conections is compared to
+the *g*-function obtained using a boundary condition of uniform borehole wall
+temperature.
+
+The script is located in: 
+`pygfunction/examples/mixed_inlet_conditions.py`
+
+.. literalinclude:: ../../pygfunction/examples/mixed_inlet_conditions.py
+   :language: python
+   :linenos:
+
+.. rubric:: References
+.. [1] Cimmino, M. (2018). g-Functions for bore fields with mixed parallel and
+   series connections considering the axial fluid temperature variations.
+   IGSHPA Research Track, Stockholm. In review.

pygfunction/boreholes.py

@@ -481,3 +481,76 @@ def visualize_field(borefield):
     plt.tight_layout(rect=[0, 0.0, 0.95, 1.0])
 
     return fig
+
+
+def _path_to_inlet(bore_connectivity, bore_index):
+    """
+    Returns the path from a borehole to the bore field inlet.
+
+    This function raises an error if the supplied borehole connectivity is
+    invalid.
+
+    Parameters
+    ----------
+    bore_connectivity : list
+        Index of fluid inlet into each borehole. -1 corresponds to a borehole
+        connected to the bore field inlet.
+    bore_index : int
+        Index of borehole to evaluate path.
+
+    Returns
+    -------
+    path : list
+        List of boreholes leading to the bore field inlet, starting from
+        borehole bore_index
+
+    """
+    # Initialize path
+    path = [bore_index]
+    # Index of borehole feeding into borehole (bore_index)
+    index_in = bore_connectivity[bore_index]
+    # Stop when bore field inlet is reached (index_in == -1)
+    while not index_in == -1:
+        # Add index of upstream borehole to path
+        path.append(index_in)
+        # Get index of next upstream borehole
+        index_in = bore_connectivity[index_in]
+
+    return path
+
+
+def _verify_bore_connectivity(bore_connectivity, nBoreholes):
+    """
+    Verifies that borehole connectivity is valid.
+
+    This function raises an error if the supplied borehole connectivity is
+    invalid.
+
+    Parameters
+    ----------
+    bore_connectivity : list
+        Index of fluid inlet into each borehole. -1 corresponds to a borehole
+        connected to the bore field inlet.
+    nBoreholes : int
+        Number of boreholes in the bore field.
+
+    """
+    if not len(bore_connectivity) == nBoreholes:
+        raise ValueError(
+            'The length of the borehole connectivity list does not correspond '
+            'to the number of boreholes in the bore field.')
+    # Cycle through each borehole and verify that connections lead to -1
+    # (-1 is the bore field inlet)
+    for i in range(nBoreholes):
+        n = 0 # Initialize step counter
+        # Index of borehole feeding into borehole i
+        index_in = bore_connectivity[i]
+        # Stop when bore field inlet is reached (index_in == -1)
+        while not index_in == -1:
+            index_in = bore_connectivity[index_in]
+            n += 1 # Increment step counter
+            # Raise error if n exceeds the number of boreholes
+            if n > nBoreholes:
+                raise ValueError(
+                    'The borehole connectivity list is invalid.')
+    return

pygfunction/examples/bore_field_thermal_resistance.py

@@ -0,0 +1,136 @@
+# -*- coding: utf-8 -*-
+""" Example of calculation of effective bore field thermal resistance.
+
+    The effective bore field thermal resistance of fields of up to 5 boreholes
+    of equal lengths connected in series is calculated for various fluid flow
+    rates.
+
+"""
+from __future__ import division, print_function, absolute_import
+
+import matplotlib.pyplot as plt
+from matplotlib.ticker import AutoMinorLocator
+import numpy as np
+from scipy import pi
+
+import pygfunction as gt
+
+
+def main():
+    # -------------------------------------------------------------------------
+    # Simulation parameters
+    # -------------------------------------------------------------------------
+
+    # Number of boreholes
+    nBoreholes = 5
+    # Borehole dimensions
+    D = 4.0             # Borehole buried depth (m)
+    # Borehole length (m)
+    H = 150.
+    r_b = 0.075         # Borehole radius (m)
+    B = 7.5             # Borehole spacing (m)
+
+    # Pipe dimensions
+    rp_out = 0.02       # Pipe outer radius (m)
+    rp_in = 0.015       # Pipe inner radius (m)
+    D_s = 0.05          # Shank spacing (m)
+    epsilon = 1.0e-6    # Pipe roughness (m)
+
+    # Pipe positions
+    # Single U-tube [(x_in, y_in), (x_out, y_out)]
+    pos_pipes = [(-D_s, 0.), (D_s, 0.)]
+
+    # Ground properties
+    k_s = 2.0           # Ground thermal conductivity (W/m.K)
+
+    # Grout properties
+    k_g = 1.0           # Grout thermal conductivity (W/m.K)
+
+    # Pipe properties
+    k_p = 0.4           # Pipe thermal conductivity (W/m.K)
+
+    # Fluid properties
+    # Total fluid mass flow rate per borehole (kg/s), from 0.01 kg/s to 1 kg/s
+    m_flow_boreholes = 10**np.arange(-2, 0.001, 0.05)
+    cp_f = 4000.        # Fluid specific isobaric heat capacity (J/kg.K)
+    den_f = 1015.       # Fluid density (kg/m3)
+    visc_f = 0.002      # Fluid dynamic viscosity (kg/m.s)
+    k_f = 0.5           # Fluid thermal conductivity (W/m.K)
+
+    # -------------------------------------------------------------------------
+    # Borehole field
+    # -------------------------------------------------------------------------
+
+    boreField = []
+    bore_connectivity = []
+    for i in range(nBoreholes):
+        x = i*B
+        borehole = gt.boreholes.Borehole(H, D, r_b, x, 0.)
+        boreField.append(borehole)
+        # Boreholes are connected in series: The index of the upstream
+        # borehole is that of the previous borehole
+        bore_connectivity.append(i - 1)
+
+    # -------------------------------------------------------------------------
+    # Evaluate the effective bore field thermal resistance
+    # -------------------------------------------------------------------------
+
+    # Initialize result array
+    R = np.zeros((nBoreholes, len(m_flow_boreholes)))
+    for i in range(nBoreholes):
+        for j in range(len(m_flow_boreholes)):
+            nBoreholes = i + 1
+            m_flow = m_flow_boreholes[j]
+
+            # Pipe thermal resistance
+            R_p = gt.pipes.conduction_thermal_resistance_circular_pipe(
+                    rp_in, rp_out, k_p)
+            # Fluid to inner pipe wall thermal resistance (Single U-tube)
+            h_f = gt.pipes.convective_heat_transfer_coefficient_circular_pipe(
+                    m_flow, rp_in, visc_f, den_f, k_f, cp_f, epsilon)
+            R_f = 1.0/(h_f*2*pi*rp_in)
+
+            # Single U-tube, same for all boreholes in the bore field
+            UTubes = []
+            for borehole in boreField:
+                SingleUTube = gt.pipes.SingleUTube(pos_pipes, rp_in, rp_out,
+                                                   borehole, k_s, k_g, R_f + R_p)
+                UTubes.append(SingleUTube)
+
+            # Effective bore field thermal resistance
+            R_field = gt.pipes.field_thermal_resistance(
+                    UTubes[:nBoreholes], bore_connectivity[:nBoreholes],
+                    m_flow, cp_f)
+            # Add to result array
+            R[i,j] = R_field
+
+    # -------------------------------------------------------------------------
+    # Plot bore field thermal resistances
+    # -------------------------------------------------------------------------
+
+    plt.rc('figure')
+    fig = plt.figure()
+    ax1 = fig.add_subplot(111)
+    # Bore field thermal resistances
+    ax1.plot(m_flow_boreholes, R[0,:], 'k-', lw=1.5, label='1 borehole')
+    ax1.plot(m_flow_boreholes, R[2,:], 'r--', lw=1.5, label='3 boreholes')
+    ax1.plot(m_flow_boreholes, R[4,:], 'b-.', lw=1.5, label='5 boreholes')
+    ax1.legend()
+    # Axis labels
+    ax1.set_xlabel(r'$\dot{m}$ [kg/s]')
+    ax1.set_ylabel(r'$R^*_{field}$ [m.K/W]')
+    # Axis limits
+    ax1.set_xlim([0., 1.])
+    ax1.set_ylim([0., 1.])
+    # Show minor ticks
+    ax1.xaxis.set_minor_locator(AutoMinorLocator())
+    ax1.yaxis.set_minor_locator(AutoMinorLocator())
+    # Adjust to plot window
+    plt.tight_layout()
+
+    return
+
+
+# Main function
+if __name__ == '__main__':
+    main()