Faster Convergence of Thermodynamic Equations of Wet Air Using Δ and K Methods

Generally, Mine ventilation is based on the analysis of fluids. The main fluid in mine ventilation is air fluid. Based on the science of fluids, air-fluid shows different behaves in different conditions. In the fluid analysis method of the ventilation science, air-fluid can be analyzed from several different perspectives such as dry model, wet model, incompressible model, and compressible model. Researchers have used various models of fluid analysis in mine ventilation and most of them believe that the real conditions for designing mine ventilation are to consider two conditions: humid air and compressible fluid analysis. Accordingly, in this paper, different fluid analysis conditions were considered for designing mine ventilation and the results show that compressible fluid analysis for humid air needs to be solved by two nonlinear equations. Therefore, it requires numerical calculation methods. One of the most common methods in numerical calculations is the Newton-Raphson method. This method is defined based on the derivative. Using this method for solving these nonlinear equations increases the volume of mathematical calculations. Therefore, in this paper, two Delta (Δ) and K methods are presented to facilitate the solution of these two nonlinear equations and reduce the error of mathematical calculations. Delta (Δ) and K methods have been defined based on thermodynamic rules for analyzing compressible humid air in mine ventilation design. Also, the amount of evaporation rate of water should be known in these methods. The results show that these two methods have a simpler and better performance.