ANALYSIS OF LOW-TEMPERATURE EXPANSION PROCESSES OF NON-IDEAL GASES

An energy analysis of the processes of obtaining and using artificial cold in chemical technology is presented. The most well-known methods of obtaining and applying the cooling effect are considered: adiabatic expansion of vapor and gaseous bodies in expanders, throttling. Special attention is paid to the effect of object deviation from the ideal gas model.

Analysis of the mathematical modelling of a static expansion system

Static expansion systems are used to generate pressures in medium and high vacuum and are used in the calibration of absolute pressure meters in these pressure ranges. In the present study, the suitability of different models to represent the final pressures in a static expansion system with two tanks is analysed. It is concluded that the use of the ideal gas model is adequate in most simulated conditions, while the assumption that the residual pressure is zero before expansion presents problems under certain conditions. An uncertainty analysis of the process is carried out, which leads to evidence of the high importance of uncertainty in a first expansion over subsequent expansion processes. Finally, an analysis of the expansion system based on uncertainty is carried out to estimate the effect of the metrological characteristics of the measurements of the input quantities. Said design process can make it possible to determine a set of restrictions on the uncertainties of the input quantities.

Adsorption of an Ideal Gas on a Small Spherical Adsorbent

The ideal gas model is an important and useful model in classical thermodynamics. This remains so for small systems. Molecules in a gas can be adsorbed on the surface of a sphere. Both the free gas molecules and the adsorbed molecules may be modeled as ideal for low densities. The adsorption energy, Us, plays an important role in the analysis. For small adsorbents this energy depends on the curvature of the adsorbent. We model the adsorbent as a sphere with surface area Ω=4πR2, where R is the radius of the sphere. We calculate the partition function for a grand canonical ensemble of two-dimensional adsorbed phases. When connected with the nanothermodynamic framework this gives us the relevant thermodynamic variables for the adsorbed phase controlled by the temperature T, surface area Ω, and chemical potential μ. The dependence of intensive variables on size may then be systematically investigated starting from the simplest model, namely the ideal adsorbed phase. This dependence is a characteristic feature of small systems which is naturally expressed by the subdivision potential of nanothermodynamics. For surface problems, the nanothermodynamic approach is different, but equivalent to Gibbs’ surface thermodynamics. It is however a general approach to the thermodynamics of small systems, and may therefore be applied to systems that do not have well defined surfaces. It is therefore desirable and useful to improve our basic understanding of nanothermodynamics.

Experimental Investigation and Theoretical Modelling of a High-Pressure Pneumatic Catapult Considering Dynamic Leakage and Convection

A high-pressure pneumatic catapult works under extreme boundaries such as high-pressure and rapid change of pressure and temperature, with the features of nonlinearity and gas-solid convection. In the thermodynamics processes, the pressure is much larger than the critical pressure, and the compressibility factor can deviate from the Zeno line significantly. Therefore, the pneumatic performance and thermo-physical properties need to be described with the real gas hypothesis instead of the ideal gas one. It is found that the analytical results based on the ideal gas model overestimate the performance of the catapult, in comparison to the test data. To obtain a theoretical model with dynamic leakage compensation, leakage tests are carried out, and the relationship among the leakage rate, pressure and stroke is fitted. The compressibility factor library of the equation of state for compressed air is established and evaluated by referring it to the Nelson-Obert generalized compressibility charts. Based on the Peng–Robinson equation, a theoretical model of the high-pressure pneumatic catapult is developed, in which the effects of dynamic leakage and the forced convective heat transfer between the gas and the metal wall are taken into account. The results from the theoretical model are consistent with the data from ejection tests. This research presents an approach to study the performance of a high-pressure pneumatic catapult with high precision.

In-Cylinder Temperature Measurements in a 55-cm3 Two-Stroke Engine Via Tunable Laser Absorption Spectroscopy

In-cylinder temperature is a critical quantity for modeling and understanding combustion dynamics in internal combustion engines (ICEs). It is difficult to measure in small, two-stroke engines due to high operational speeds and limited space to install instrumentation. Optical access was established in a 55-cm3 displacement two-stroke engine using M4 bolts as carriers for sapphire rods to establish a 1.5-mm diameter optical path through the combustion chamber. Temperature laser absorption spectroscopy was successfully used to measure time varying in-cylinder temperature clocked to the piston position with a resolution of 3.6 crank angle degrees (CAD) at 6000 rpm. The resulting temperature profiles clearly showed the traverse of the flame front and were qualitatively consistent with in-cylinder pressure, engine speed, and delivery ratio. The temperature measurements were compared to aggregate in-cylinder temperatures calculated using the ideal gas model using measured in-cylinder pressure and trapped mass calculated at exact port closure as inputs. The calculation was sensitive to the trapped mass determination, and the results show that using the ideal gas model for in-cylinder temperature calculations in heat flux models may fail to capture trends in actual in-cylinder temperature with changing engine operating conditions.

Real Gas Models in Coupled Algorithms Numerical Recipes and Thermophysical Relations

In the majority of compressible flow CFD simulations, the standard ideal gas state equation is accurate enough. However, there is a range of applications where the deviations from the ideal gas behaviour is significant enough that performance predictions are no longer valid and more accurate models are needed. While a considerable amount of the literature has been written about the application of real gas state equations in CFD simulations, there is much less information on the numerical issues involved in the actual implementation of such models. The aim of this article is to present a robust implementation of real gas flow physics in an in-house, coupled, pressure-based solver, and highlight the main difference that arises as compared to standard ideal gas model. The consistency of the developed iterative procedures is demonstrated by first comparing against results obtained with a framework using perfect gas simplifications. The generality of the developed framework is tested by using the parameters from two different real gas state equations, namely the IAPWS-97 and the cubic state equations state equations. The highly polynomial IAPWS-97 formulation for water is applied to a transonic nozzle case where steam is expanded at transonic conditions until phase transition occurs. The cubic state equations are applied to a two stage radial compressor setup. Results are compared in terms of accuracy with a commercial code and measurement data. Results are also compared against simulations using the ideal gas model, highlighting the limitations of the later model. Finally, the effects of the real gas formulations on computational time are compared with results obtained using the ideal gas model.

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.