Carnot Engine: A New Look with Different Real Gas Equations

The efficiency of Carnot engine, an important machine in classical thermodynamics, depends only on the temperatures of source and sink reservoirs and is independent of the nature of the working substance. There are several real gas equations which may be used to verify this statement. Here we choose three real gas equations viz. Van der Waal’s, Berthelot’s and Clausius’s real gas equation of state for simplicity for this verification.

Mathematical Model of Small-Volume Air Vessel Based on Real Gas Equation

The gas characteristics of an air vessel is one of the key parameters that determines the protective effect on water hammer pressure. Because of the limitation of the ideal gas state equation applied for a small-volume vessel, the Van der Waals (VDW) equation and Redlich–Kwong (R–K) equation are proposed to numerically simulate the pressure oscillation. The R–K polytropic equation is derived under the assumption that the volume occupied by the air molecules themselves could be ignored. The effects of cohesion pressure under real gas equations are analyzed by using the method of characteristics under different vessel diameters. The results show that cohesion pressure has a significant effect on the small volume vessel. During the first phase of the transient period, the minimum pressure and water depth calculated by a real gas model are obviously lower than that calculated by an ideal gas model. Because VDW cohesion pressure has a stronger influence on the air vessel pressure compared to R–K air cohesion pressure, the amplitude of head oscillation in the vessel calculated by the R–K equation becomes larger. The numerical results of real gas equations can provide a higher safe-depth margin of the water depth required in the small-volume vessel, resulting in the safe operation of the practical pumping pipeline system.

Coupled Physics Performance Predictions and Risk Assessment for Dry Gas Seal Operating in MW-Scale Supercritical CO2 Turbine

U.S. Department of Energy (DOE) has recently sponsored research programs to develop megawatt scale supercritical CO2 (sCO2) turbine for use in concentrated solar power (CSP) and fossil based applications. To achieve the CSP goal of power at $0.06/kW-hr LCOE and energy conversion efficiency > 50%, the sCO2 turbine relies critically on extremely low leakage film riding seals like dry gas seal (DGS). Although DGS technology has been used in other applications before. making it successful for stringent conditions of an sCO2 turbo-expander is challenging. This paper presents results from a multi-scale coupled physics model that predicts the performance of DGS under a typical sCO2 turbine mission cycle and addresses some of the risks specific to operation in sCO2. Real gas equations of state are incorporated in the models to capture large discontinuities in fluid properties close to the critical point. A novel experimental setup is developed to observe and characterize transition of CO2 through liquid-vapor and supercritical phases. Coupled fluid-structure-thermal interaction model investigates the effect of aerodynamic and thermal perturbations on the structural and rotordynamic instabilities. Dynamic instabilities arising from sonic transition in thin sCO2 film of DGS pose additional challenges while the large surface roughness changes due to sCO2 corrosion warrant further design considerations. Effectiveness of features like spiral grooves in converting fluid momentum into pressure rise in the thin film and also in achieving local flow reversals is investigated. Effect of various design features on the optimal performance is quantified and insights for a successful DGS operation in a sCO2 turbomachine are provided.

Numerical Simulation of the Filling-Up Process of a Hydrogen Fuel Tank for Vehicular Applications

Hydrogen holds much promise as a source of energy that is at once abundant, clean, flexible, and secure. It is also environment friendly because it burns without producing carbon dioxide. Physical characteristics of hydrogen make it difficult to store in large quantities without taking up large amount of space. High pressure gas is a widely used storage mode for hydrogen fuel. Filling up process of a high pressure hydrogen tank should be reasonably short. The process should be designed so as to avoid high temperatures in the tank because of safety reasons. Numerical simulation can aid in optimizing the filling up process. The paper reports the numerical simulation of the filling up process of hydrogen tanks using computational fluid dynamics method. Real gas equations are solved to accurately simulate the process at the high temperature and pressure associated with the fast filling. Local temperature distribution in the tank is obtained at different durations of the fill. The numerical results obtained are validated with available experimental data.