Numerical investigation of forced convection from vertical boreholes

Abstract In this work, the transient forced convection from vertical boreholes is investigated by numerical simulation. The actual borehole geometry is accounted for, resulting in perturbed flow and temperature fields. The present results are compared with an analytical line heat source model. A wide range of viable Peclet numbers is considered. The predicted average borehole surface temperature, Θ ¯ b , is in excellent agreement with the analytical solution for Pe ≲ 0.2 and Fo ≳ 1. As in the infinite line source model heat is released from the borehole axis so that the rise of the average borehole temperature provided by the analytical model is slower than the present results for Fo   0.2, the distortion of the flow field induced by the borehole shows a significant effect on Θ ¯ b , causing an appreciable difference between the numerical results and the analytical solution in the whole range of considered Fourier numbers.

[1]  Louis Lamarche,et al.  A new contribution to the finite line-source model for geothermal boreholes , 2007 .

[2]  C. L. Tien,et al.  Boundary and inertia effects on flow and heat transfer in porous media , 1981 .

[3]  J. Bear Dynamics of Fluids in Porous Media , 1975 .

[4]  J. C. Jaeger,et al.  Conduction of Heat in Solids , 1952 .

[5]  K. Zhu,et al.  A moving finite line source model to simulate borehole heat exchangers with groundwater advection , 2011 .

[6]  Marzio Piller,et al.  Compact finite volume schemes on boundary-fitted grids , 2008, J. Comput. Phys..

[7]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[8]  A. Bejan,et al.  Convection in Porous Media , 1992 .

[9]  P. Blum,et al.  Evaluating the influence of thermal dispersion on temperature plumes from geothermal systems using analytical solutions , 2011 .

[10]  M. Piller,et al.  Development of a mixed control volume - Finite element method for the advection-diffusion equation with spectral convergence , 2011 .

[11]  O. J. Zobel,et al.  Heat conduction with engineering, geological, and other applications , 1955 .

[12]  Z. Fang,et al.  A finite line‐source model for boreholes in geothermal heat exchangers , 2002 .

[13]  R. E. Collins Flow of fluids through porous materials , 1961 .

[14]  M. Piller,et al.  Numerical investigation of natural convection in inclined parallel-plate channels partly filled with metal foams , 2012 .

[15]  M. Bernier,et al.  Validity ranges of three analytical solutions to heat transfer in the vicinity of single boreholes , 2009 .

[16]  S. Whitaker The method of volume averaging , 1998 .

[17]  H.-J. G. Diersch,et al.  Transient 3D analysis of borehole heat exchanger modeling , 2011 .

[18]  Philippe Pasquier,et al.  Fast fluid and ground temperature computation for geothermal ground-loop heat exchanger systems , 2008 .

[19]  F. B. Introduction to Bessel Functions , 1939, Nature.

[20]  Mostafa H. Sharqawy,et al.  Effective pipe-to-borehole thermal resistance for vertical ground heat exchangers , 2009 .

[21]  D. Nutter,et al.  A Ground Resistance for Vertical Bore Heat Exchangers With Groundwater Flow , 2003 .

[22]  Philippe Pasquier,et al.  The importance of axial effects for borehole design of geothermal heat-pump systems , 2010 .

[23]  A. Philippacopoulos,et al.  Influence of debonding in ground heat exchangers used with geothermal heat pumps , 2001 .

[24]  Stanislaw Kajl,et al.  A review of methods to evaluate borehole thermal resistances in geothermal heat-pump systems , 2010 .

[25]  Ryuichi Itoi,et al.  Optimizing the design of large-scale ground-coupled heat pump systems using groundwater and heat transport modeling , 2005 .

[26]  Jeffrey D. Spitler,et al.  A computationally efficient hybrid time step methodology for simulation of ground heat exchangers , 2011 .

[27]  Kimura Shigeo Transient forced convection heat transfer from a circular cylinder in a saturated porous medium , 1989 .

[28]  Göran Hellström,et al.  Influence on thermal response test by groundwater flow in vertical fractures in hard rock , 2003 .

[29]  Georgios A. Florides,et al.  Ground heat exchangers—A review of systems, models and applications , 2007 .

[30]  Z. Fang,et al.  Heat transfer in ground heat exchangers with groundwater advection , 2004 .

[31]  Per Eskilson Thermal analysis of heat extraction boreholes , 1987 .

[32]  Yang Yao,et al.  A study on the performance of a geothermal heat exchanger under coupled heat conduction and groundwater advection , 2007 .

[33]  Y. Gu,et al.  Development of an equivalent diameter expression for vertical U-tubes used in ground-coupled heat pumps , 1998 .

[34]  Kambiz Vafai,et al.  Convective flow and heat transfer in variable-porosity media , 1984, Journal of Fluid Mechanics.

[35]  S. Rees,et al.  A preliminary assessment of the effects of groundwater flow on closed-loop ground source heat pump systems , 2000 .

[36]  Stefan Finsterle,et al.  A time-convolution approach for modeling heat exchange between a wellbore and surrounding formation , 2011 .

[37]  Stephen P. Kavanaugh,et al.  Ground Source Heat Pumps : Design of Geothermal Systems for Commercial and Institutional Buildings , 1997 .