Integral equation solution for three‐dimensional heat transfer in multiple‐fracture enhanced geothermal reservoirs

2020 ◽  
Vol 44 (11) ◽  
pp. 1511-1524
Author(s):  
Dong Dong Liu ◽  
Yan Yong Xiang ◽  
Jin Lei Zheng
Keyword(s):  
Heat Transfer ◽  
Integral Equation ◽  
Three Dimensional ◽  
Multiple Fracture ◽  
Equation Solution ◽  
Geothermal Reservoirs ◽  
Enhanced Geothermal Reservoirs

Coupled BEM and FDM Conjugate Analysis of a Three-Dimensional Air-Cooled Turbine Vane

2009 ◽  
Author(s):  
Zhenfeng Wang ◽  
Peigang Yan ◽  
Hongyan Huang ◽  
Wanjin Han
Keyword(s):  
Heat Transfer ◽  
Integral Equation ◽  
Conjugate Heat Transfer ◽  
Analytic Solution ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Surface Integral ◽  
Surface Integral Equation ◽  
Commercial Code ◽  
Good Agreement

A coupled boundary element method (BEM) and finite difference method (FDM) are applied to solve conjugate heat transfer problem of a three-dimensional air-cooled turbine blade. A loosely coupled strategy is adopted, in which each set of field equations is solved to provide boundary conditions for the other. In the fluid region, computation code (HIT-NS CODE) adopts the FDM to solve the Navier-Stokes equations. In the solid region, the BEM is adopted to resolve the conduction heat transfer equations. An iterated convergence criterion is the continuity of temperature and heat flux at the fluid-solid interface. The solid heat transfer computation code (3D-BEM CODE) is validated by comparing with the results of an analytic solution and the results of commercial code, the results from 3D-BEM CODE have a good agreement with the analytic solution and commercial code results. The BEM uses a weighted residual method to make the Laplace equation convert into a surface integral equation and the surface integral equation is discretized. The BEM avoids the complicated mesh needed in other computation methods and saves the computation time. In addition, the BEM has the characteristic of a combination of an analytic and a discrete solution. So the BEM solutions of heat conduction problems are more accurate. The results of the coupling computation code (HIT-NS-3DBEM CODE) have a good agreement with the experimental results. The adiabatic condition result is different from the results of experiment and code calculation. So the results from conjugate heat transfer analysis are more accurate and they are closer to realistic thermal environment of turbines. Four turbulence models are applied: K-epsilon model, K-omega model, K-omega (SST-Gamma Theta) model, and B-L model adopted by computation code. Different turbulence models gives different the results of vane wall temperature. Comparing the four turbulence models, the different turbulence models can exactly simulate the flow field, but they can not give exact values for the heat conduction simulation in the boundary layer. The result of K-Omega (SST-Gamma Theta) turbulence model is closer to the experimental data.

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