Constructal Design Applied to the Geometric Evaluation of a T-Shaped Earth-Air Heat Exchanger

An Earth-Air Heat Exchanger (EAHE) is a device that consists of one or more buried ducts through which air is forced to flow. The surrounding soil is responsible for enabling thermal exchanges along with the installation, making the temperature at the outlet milder than the inlet. The objective of this work is to ally a numerical-analytical approach with the Constructal Design method and Exhaustive Search technique to minimize the soil volume occupation (V), minimize the air flow pressure drop (PD), and maximize the thermal potential (TP) of a T-shaped EAHE. Starting from a conventional EAHE composed of a straight duct, called Reference Installation (RI), two degrees of freedom (DOF) were considered: the ratio between the length of the bifurcated branch and the length of the main branch (L1/L0) and the ratio between the diameter of the bifurcated branch and the diameter of the main branch (D1/D0). Comparing with RI, different T-shaped EAHE geometries were identified to reduce V by 23% and PD by 62% and to increase TP by 21%; and when these three performance parameters were concomitantly considered another T-shaped EAHE geometric configuration allowed to reach an improvement of around 27% when compared with the RI.

U-duct turbulent-flow computation with the ST-VMS method and isogeometric discretization

The U-duct turbulent flow is a known benchmark problem with the computational challenges of high Reynolds number, high curvature and strong flow dependence on the inflow profile. We use this benchmark problem to test and evaluate the Space–Time Variational Multiscale (ST-VMS) method with ST isogeometric discretization. A fully-developed flow field in a straight duct with periodicity condition is used as the inflow profile. The ST-VMS serves as the core method. The ST framework provides higher-order accuracy in general, and the VMS feature of the ST-VMS addresses the computational challenges associated with the multiscale nature of the unsteady flow. The ST isogeometric discretization enables more accurate representation of the duct geometry and increased accuracy in the flow solution. In the straight-duct computations to obtain the inflow velocity, the periodicity condition is enforced with the ST Slip Interface method. All computations are carried out with quadratic NURBS meshes, which represent the circular arc of the duct exactly in the U-duct computations. We investigate how the results vary with the time-averaging range used in reporting the results, mesh refinement, and the Courant number. The results are compared to experimental data, showing that the ST-VMS with ST isogeometric discretization provides good accuracy in this class of flow problems.

Heat Transfer Characteristics of Non-Uniform Flow Around a Circular Cylinder in a T-Junction Duct

Heat transfer characteristics of a circular cylinder in the branch of a T-junction are experimentally investigated in a low-speed wind tunnel with Reynolds number of Rec = 9163. Local and average heat transfer distributions around the circular cylinder are obtained for the cylinder positions from x/Dh=0.5 to 13 and the velocity ratios from 0.117 to 0.614. It is found that the overall heat transfer characteristics in a T-junction duct at high velocity ratio are lower than those at low velocity ratio, and both are higher than those in the straight duct. The local Nusselt number in the T-junction duct is asymmetrical distribution and weakens with increasing velocity ratios and positions of the cylinder. The angles of the front and rear stagnation points in the T-junction duct are the same as those in the straight duct at certain velocity ratio and/or position of the cylinder. However, the angles of the front and rear separation points in the T-junction duct do not match those in the straight duct. Both the heat transfer correlation coefficients and the amplitude ratios increase with increasing positions of the circular cylinder and velocity ratios.

Large-Eddy and RANS Simulations of Heat Transfer in a U-Duct With a High-Aspect Ratio Trapezoidal Cross Section

Large-eddy and RANS simulations were performed to examine the details of the heat-transfer mechanisms in a U-duct with a high-aspect ratio trapezoidal cross section at a Reynolds number of 20,000. ANSYS-Fluent was used to perform the simulations. For the large-eddy simulations (LES), the WALE subgrid-scale model was employed, and its inflow boundary condition was provided by a concurrent LES of incompressible fully-developed flow in a straight duct with the same cross section and flow conditions as the U-duct. The grid resolution required to obtain meaningful LES solutions were obtained via a grid sensitivity study of incompressible fully-developed turbulent flow in a straight duct of square cross section, where data from direct numerical simulation (DNS) and experiments are available to validate and guide the simulation. In addition, the grid used satisfies Celik’s criterion, and resolves the Kolmogorov’s −5/3 law. Results were also obtained for the U-duct by using RANS, and three widely used turbulence models were examined — realizable k-ε with the two-layer model in the near-wall region, shear-stress transport (SST) model, and stress-omega full Reynolds stress model (RSM). Results obtained from LES showed unsteady flow separation to occur immediately after the turn region, which none of the RANS models could predict. By being able to capture this unsteady flow mechanism, LES was able to predict the measured heat-transfer downstream of the U-duct. The maximum relative error in the predicted local heat-transfer coefficient was less than 10% in the LES results, but up to 80% in the RANS results.