.BuildingSystems.Fluid.Geothermal.Borefields.BaseClasses.Boreholes.BaseClasses.Functions.convectionResistanceCircularPipe

Information

This model computes the convection resistance in the pipes of a borehole segment with heigth h_Seg using correlations suggested by Bergman et al. (2011).

If the flow is laminar (Re ≤ 2300, with Re being the Reynolds number of the flow), the Nusselt number of the flow is assumed to be constant at 3.66. If the flow is turbulent (Re > 2300), the correlation of Dittus-Boelter is used to find the convection heat transfer coefficient as

Nu = 0.023   Re^0.8   Prⁿ,

where Nu is the Nusselt number and Pr is the Prandlt number. A value of n=0.35 is used, as the reference uses n=0.4 for heating and n=0.3 for cooling. To ensure that the function is continuously differentiable, a smooth transition between the laminar and turbulent values is created for the range 2300 < Re < 2400.

References

Bergman, T. L., Incropera, F. P., DeWitt, D. P., & Lavine, A. S. (2011). Fundamentals of heat and mass transfer (7th ed.). New York: John Wiley & Sons.

Interface

function convectionResistanceCircularPipe
  extends Modelica.Icons.Function;
  input Modelica.Units.SI.Height hSeg "Height of the element";
  input Modelica.Units.SI.Radius rTub "Tube radius";
  input Modelica.Units.SI.Length eTub "Tube thickness";
  input Modelica.Units.SI.ThermalConductivity kMed "Thermal conductivity of the fluid";
  input Modelica.Units.SI.DynamicViscosity muMed "Dynamic viscosity of the fluid";
  input Modelica.Units.SI.SpecificHeatCapacity cpMed "Specific heat capacity of the fluid";
  input Modelica.Units.SI.MassFlowRate m_flow "Mass flow rate";
  input Modelica.Units.SI.MassFlowRate m_flow_nominal "Nominal mass flow rate";
  output Modelica.Units.SI.ThermalResistance RFluPip "Convection resistance (or conduction in fluid if no mass flow)";
end convectionResistanceCircularPipe;

Revisions

• June 4, 2023, by Michael Wetter:
  Corrected variability.
  This is for IBPSA, #1762.
• July 10, 2018, by Alex Laferrière:
  Added laminar flow and smooth laminar-turbulent transition. Revised documentation.
• February 14, 2014, by Michael Wetter:
  Removed unused input rBor. Revised documentation.
• January 24, 2014, by Michael Wetter:
  Revised implementation. Changed cpFluid to cpMed to use consistent notation. Added regularization for computation of convective heat transfer coefficient to avoid an event and a non-differentiability.
• January 23, 2014, by Damien Picard:
  First implementation.