SUMMARYA method of reducing the number of degrees of freedom and the overall computing times in finite element method (FEM) has been devised. The technique is valid for linear problems and arbitrary temporal variation of boundary conditions. At the first stage of the method standard FEM time stepping procedure is invoked. The temperature fields obtained for the first few time steps undergo statistical analysis yielding an optimal set of globally defined trial and weighting functions for the Galerkin solution of the problem at hand. Simple matrix manipulations applied to the original FEM system produce a set of ordinary differential equations of a dimensionality greatly reduced when compared with the original FEM formulation. Using the concept of modal analysis the set is then solved analytically. Treatment of non-homogeneous initial conditions, time-dependent boundary conditions and controlling the error introduced by the reduction of the degrees of freedom are discussed. Several numerical examples are included for validation of the approach.
Application range of the HEM approach for CO 2 expansion inside two-phase ejectors for supermarket refrigeration systems, International Journal of Refrigeration (2015), http://dx.doi.org/
HighlightsThe accuracy of the HEM approach for the R744 expansion inside ejectors was assessed.The HEM accuracy decrease with the decreasing motive nozzle inlet temperature.The HEM guarantee accurate results for operating regimes close to the CO2 critical point.
AbstractIn this study, the accuracy of the homogeneous equilibrium (HEM) applied to 3-D CFD-based simulations of CO 2 expansion inside two-phase ejectors is presented. The HEM approach previously reported in the literature were assessed by comparing the computed and measured mass flow rates that pass through an ejector motive nozzle. In addition, the HEM approach implemented using CFD was tested over a vast range of ejector operating regimes. To ensure that all of the computations were performed consistently, a validated CFD model combined within an in-house developed script was used. The comparison of the experimental and computational results showed that the HEM accuracy varied for the different sets of operating parameters. Accurate results were obtained for operating regimes near or above the CO 2 critical point. The model accuracy decreased with the decreasing temperature and decreasing distance to the saturation line.
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