Real Gas Properties Research Articles

Identification and thermodynamic analysis of reaction pathways of methylal and OME-n formation

Renewable energy from wind and solar sources is affected by fluctuations which do not correspond to the demand for electrical energy. Storage options are therefore required and also other possibilities of utilizing this power in a future energy system. Fuel synthesis using CO2 from industrial waste gases and hydrogen from electrolysis is an attractive approach. Methylal and higher oxymethylene ethers represent one fuel option due to the low-emission combustion of ethers with their characteristic CO bonds. However, conventional synthesis is an elaborate process because of the large number of intermediate steps. The direct synthesis of methylal and higher oxymethylene ethers would considerably simplify the technical implementation. Here we present a method that considers Gibbs energy in order to analyze the possibilities of direct synthesis from CO2-H2. High operating pressures and influence of the critical states of educt and products on the thermodynamic state parameters of enthalpy and entropy mean that the real gas properties can be modeled by an equation of state. Methylal can be formed with high conversion rates at pressures of 100 bar and temperatures below 373 K. Formation of dimethyl ether as a potential by-product must be suppressed by a suitable catalyst since it is thermodynamically favored.

A mean-line model to predict the design efficiency of radial inflow turbines in organic Rankine cycle (ORC) systems

Organic Rankine Cycle (ORC) systems represent an efficient technology for power generation from low-to-medium temperature heat sources. Most of the efforts in the recent literature are addressed to the improvement of turbine design and efficiency by taking advantage of the low enthalpy drops while dealing with the large volume flow ratios across the expansion process and low speed of sound typical of high molecular weight fluids. These peculiar conditions make the choice and the design of an ORC turbine a challenging task, exacerbated by the only few experimental data available in the open literature. The aim of this paper is to obtain the optimum design and corresponding maximum efficiency of single stage radial inflow turbines for different cycle design specifications (i.e., mass flow rate and enthalpy drop) using the real gas properties of refrigerant R245fa. This aim is pursued by means of a mean-line model developed in Matlab® which includes the design and performance analysis procedure suggested by Aungier (2005). Results indicate how different design choices in terms of specific speed and velocity ratio, and different working conditions in terms of expansion ratio and turbine size may affect the efficiency of single stage radial inflow turbines in ORC systems.

Assessing relative contributions of transport mechanisms and real gas properties to gas flow in nanoscale organic pores in shales by pore network modelling

It is well-known that the movement of gas in organic nanoscale pores of typical shales must be modelled by capturing real gas flow behaviours in the full range of flow regimes, gas ad-/de-sorption and its effect on the flow, and surface diffusion while properly accounting for real gas PVT and viscosity changes as affected by the confined pore space. So far, no comprehensive model has been developed to enable the evaluation of the relative contributions of each of these physical aspects in a realistic organic pore space. In this work, a steady-state pore-network gas flow model that accounts for all of the listed aspects is developed to allow an assessment of their flow contributions in organic pores. The gas flow model is applied to three pore/throat network models, which are constructed from the same realistic pore network but with different average pore radii at 15.6, 3.2 and 1.56 nanometres, respectively, to calculate apparent gas permeability for each model at gas pressures ranging from 5 to 70MPa. Analytical solution is applied to calculate the apparent gas permeability at the same gas pressures for three cylindrical pores with pore radii equal to the average pore radii of respective pore networks. For both the single pores and the pore networks, results show that when the average or single pore radius is larger than 10nm, there is little influence on apparent gas permeability no matter what gas property, either real or ideal gas, is considered, nor is the surface diffusion, in the full pressure range. However, when the pore radius is smaller than 5nm, the apparent gas permeability is notably influenced by the gas property and the surface diffusion. Furthermore when the pore radius is less than 2nm, the gas permeability will be significantly underestimated if the surface diffusion is neglected. It is found that the influence of both critical temperature and pressure in the confined pore space, which deviate from the expected values in wide space, is insignificant and negligible on shale gas permeability. The relative contributions of the gas property and the surface diffusion, respectively, are shown to follow different trends for the single pores and the pore networks within the range of the pressures. An analysis shows that the differences can be attributed to the mixture of large and small pores and throats in a pore network that effectively suppresses the stronger effects of the gas property and the surface diffusion in the smaller pores and throats. This indicates the importance to consider spatial pore size distribution and pore connectivity when seeking to estimate effective properties.

Effect of energy equation in one control-volume bulk-flow model for the prediction of labyrinth seal dynamic coefficients

Abstract The influence of sealing components on the rotordynamic stability of turbomachinery has become a key topic because the oil and gas market is increasingly demanding high rotational speeds and high efficiency. This leads the turbomachinery manufacturers to design higher flexibility ratios and to reduce the clearance of the seals. Accurate prediction of the effective damping of seals is critical to avoid instability problems; in recent years, “negative-swirl” swirl brakes have been used to reverse the circumferential direction of the inlet flow, which changes the sign of the cross-coupled stiffness coefficients and generates stabilizing forces. Experimental tests for a teeth-on-stator labyrinth seal were performed by manufacturers with positive and negative pre-swirl values to investigate the pre-swirl effect on the cross-coupled stiffness coefficient. Those results are used as a benchmark in this paper. To analyse the rotor-fluid interaction in the seals, the bulk-flow numeric approach is more time efficient than computational fluid dynamics (CFD). Although the accuracy of the coefficients prediction in bulk-flow models is satisfactory for liquid phase application, the accuracy of the results strongly depends on the operating conditions in the case of the gas phase. In this paper, the authors propose an improvement in the state-of-the-art bulk-flow model by introducing the effect of the energy equation in the zeroth-order solution to better characterize real gas properties due to the enthalpy variation along the seal cavities. The consideration of the energy equation allows for a better estimation of the coefficients in the case of a negative pre-swirl ratio, therefore, it extend the prediction fidelity over a wide range of operating conditions. The numeric results are also compared to the state-of-the-art bulk-flow model, which highlights the improvement in the model.

3D Numerical Modeling of Zeotropic Mixtures and Pure Working Fluids in an ORC Turbo-Expander

The present paper provides a numerical study that leads to the proper selection of a working fluid for use in low-temperature organic Rankine cycle (ORC) applications. This selection is not only based on the provision of best efficiency but also to comply with global warming potential (GWP) regulations. For that purpose, different pure organic working fluids, including R245fa, R236fa, R123, R600a, R134a, and R1234yf as well as zeotropic mixture R245fa/R600a, are selected. The investigation is conducted on a single stage radial inflow turbo-expander, which was originally used in the Sundstrand Power Systems T-100 Multipurpose Small Power Unit. The commercial package ANSYS-CFX (version 16.0) was used to perform the numerical study using 3D Reynolds-Averaged Navier–Stokes (RANS) simulations. Peng–Robinson equation of state is adopted in the finite-volume solver ANSYS-CFX to determine the real-gas properties. The obtained results show that, while the use of R134a and R1234yf provides the best efficiency of all the working fluids under investigation, the latter is best selected for its comparatively low global warming effects.

Моделирование аварийных режимов участка газопровода с учетом свойств реального газа

Моделирование аварийных режимов участка газопровода с учетом свойств реального газа

Optimization of two-phase R600a ejector geometries using a non-equilibrium CFD model

A vapor compression cycle, which is typically utilized for the heat pump, air conditioning and refrigeration systems, has inherent thermodynamic losses associated with expansion and compression processes. To minimize these losses and improve the energy efficiency of the vapor compression cycle, an ejector can be applied. However, due to the occurrence of complex physics i.e., non-equilibrium flashing compressible flow in the nozzle with possible shock interactions, it has not been feasible to model or optimize the design of a two-phase ejector. In this study, a homogeneous, non-equilibrium, two-phase flow computational fluid dynamics (CFD) model in a commercial code is used with an in-house empirical correlation for the mass transfer coefficient and real gas properties to perform a geometric optimization of a two-phase ejector. The model is first validated with experimental data of an ejector with R600a as the working fluid. After that, the design parameters of the ejector are optimized using multi-objective genetic algorithm (MOGA) based online approximation-assisted optimization (OAAO) approaches to find the maximum performance.

CFD Simulation of a Supercritical Carbon Dioxide Radial-Inflow Turbine, Comparing the Results of Using Real Gas Equation of Estate and Real Gas Property File

The present study explores CFD analysis of a supercritical carbon dioxide (SCO2) radial-inflow turbine generating 100kW from a concentrated solar resource of 560oC with a pressure ratio of 2.2. Two methods of real gas property estimations including real gas equation of estate and real gas property (RGP) file - generating a required table from NIST REFPROP - were used. Comparing the numerical results and time consumption of both methods, it was shown that equation of states could insert a significant error in thermodynamic property prediction. Implementing the RGP table method indicated a very good agreement with NIST REFPROP while it had slightly more computational cost compared to the RGP table method.

Experimental and Numerical Study of Supercritical Carbon Dioxide Flow Through Valves

The supercritical carbon dioxide (sCO2) Brayton cycle shows advantages such as high efficiency, compactness, and low capital cost. These benefits make it a competitive candidate for future-generation power-conversion cycles. In order to study this cycle, valve characteristics under sCO2 flow conditions must be studied. However, the traditional models for valves may not be accurate due to the real gas property of sCO2. In this study, this problem was studied both experimentally and numerically. A small valve was tested in the authors’ experiment facility first to provide validation data. For this valve, numerical predictions of mass flow rate agree with experimental data. Then, simulations were scaled up to valves in a real power-cycle design. The traditional gas-service valve model fails to predict mass flow rate at low-pressure ratios. A modification was proposed to improve the current gas-service valve model by changing the choked-flow check.

Theoretical analysis of ejector refrigeration system performance under overall modes

The ejector refrigeration integrated in the air-conditioning system is a promising technology, because it could be driven by the low grade energy. In the present study, a theoretical calculation based on the real gas property is put forward to estimate the ejector refrigeration system performance under overall modes (critical/sub-critical modes). The experimental data from literature are applied to validate the proposed model. The findings show that the proposed model has higher accuracy compared to the model using the ideal gas law, especially when the ejector operates at sub-critical mode. Then, the performances of the ejector refrigeration circle using different refrigerants are analyzed. R290 and R134a are selected as typical refrigerants by considering the aspects of COP, environmental impact, safety and economy. Finally, the ejector refrigeration performance is investigated under variable operation conditions with R290 and R134a as refrigerants. The results show that the R290 ejector circle has higher COP under critical mode and could operate at low evaporator temperature. However, the performance would decrease rapidly at high condenser temperature. The performance of R134a ejector circle is the opposite, with relatively lower COP, and higher COP at high condenser temperature compared to R290.

Transient analysis of single stage GM type double inlet pulse tube cryocooler

Transient analysis of single stage GM type double inlet pulse tube cryocooler is carried out using a one dimensional numerical model based on real gas properties of helium. The model solves continuity, momentum and energy equation for gas and solid to analyse the physical process occurring inside of the pulse tube cryocooler. Finite volume method is applied to discretize the governing equations with realistic initial and boundary conditions. Input data required for solving the model are the design data and operating parameters viz. pressure waveform from the compressor, regenerator matrix data, and system geometry including pulse tube, regenerator size and operating frequency for pulse tube cryocooler. The model investigates the effect of orifice opening, double inlet opening, pressure ratio, system geometry on no load temperature and refrigeration power at various temperatures for different charging pressure. The results are compared with experimental data and reasonable agreement is observed. The model can further be extended for designing two stage pulse tube cryocooler.

Supersonic nozzle profiling for supersonic aerospace testing in a view of high-temperature of properties of real gases

The paper presents the modified method for the supersonic nozzle profiling with respect to non-monotonic dependence of adiabatic index on temperature, as well as the results of nozzle profile calculation for two sets of input parameters, based on independently determined specific heat curve for molecular nitrogen N2 and products of its thermal decomposition in the temperature range of T = 260-100000 K and atmospheric pressure.

An Investigation of Real Gas Effects in Supercritical CO2 Centrifugal Compressors

This paper presents a comprehensive assessment of real gas effects on the performance and matching of centrifugal compressors operating in supercritical CO2. The analytical framework combines first principles based modeling with targeted numerical simulations to characterize the internal flow behavior of supercritical fluids with implications for radial turbomachinery design and analysis. Trends in gas dynamic behavior, not observed for ideal fluids, are investigated using influence coefficients for compressible channel flow derived for real gas. The variation in the properties of CO2 and the expansion through the vapor-pressure curve due to local flow acceleration are identified as possible mechanisms for performance and operability issues observed near the critical point. The performance of a centrifugal compressor stage is assessed at different thermodynamic conditions relative to the critical point using computational fluid dynamics (CFD) calculations. The results indicate a reduction of 9% in the choke margin of the stage compared to its performance at ideal gas conditions due to variations in real gas properties. Compressor stage matching is also impacted by real gas effects as the excursion in corrected mass flow per unit area from inlet to outlet increases by 5%. Investigation of the flow field near the impeller leading edge at high flow coefficients shows that local flow acceleration causes the thermodynamic conditions to reach the vapor-pressure curve. The significance of two-phase flow effects is determined through a nondimensional parameter that relates the time required for liquid droplet formation to the residence time of the flow under saturation conditions. Applying this criterion to the candidate compressor stage shows that condensation is not a concern at the investigated operating conditions. In the immediate vicinity of the critical point however, this effect is expected to become more prominent. While the focus of this analysis is on supercritical CO2 compressors for carbon capture and sequestration (CCS), the methodology is directly applicable to other nonconventional fluids and applications.

Analytic equations for the Wilson point in high-pressure steam flow through a nozzle

An analytical method for the position and flow properties of Wilson point in high-pressure steam flow through a nozzle was presented. The thermodynamic properties of real gas and essential empirical equations at high-pressure for both superheated and supercooled steam were used to solve the position of Wilson point. Firstly, the analytic equation for the isentropic flow of real gas before Wilson point was built and a two dimensional bisection method was utilized for solving this nonlinear equation. And then, combining Rayleigh flow relationships, the position and properties of Wilson point can be efficiently solved by only giving the values of the nozzle geometry, inlet stagnation pressure and temperature. The algebraic solutions are well in agreement with high-pressure experimental data by Bakhtar. The relative deviations between calculation results and experimental data for three type nozzles are 0.09–0.56%, 0.09–0.57%, and 0.56–1.20% respectively. At last, a serial of isobaric and isothermal lines for the position of Wilson point were obtained to illustrate the power of this method. This analytic method contributes to the further research of theory, simulation and experiment at high-pressure steam flow.

1D Model to Predict Ejector Performance at Critical and Sub-critical Operation in the Refrigeration System

Abstract A new 1D model using the real gas property is proposed to predict ejector performance at critical and sub-critical operational modes, while most previous 1D models usually used the ideal gas property and only predicted ejector performance at critical mode operation. Constant pressure mixing is assumed to occur inside the constant area section of the ejector at critical and sub-critical mode operation, and the effectiveness of the model is verified against experimental data. The results show that the proposed model accurately predicts ejector performance over all ranges of operation. The 1D model is a useful tool for predicting ejector performance within larger refrigeration cycle models.

Reciprocating and Screw Compressor semi-empirical models for establishing minimum energy performance standards

The efficiency bar for a Minimum Equipment Performance Standard (MEPS) generally aims to minimize energy consumption and life cycle cost of a given chiller type and size category serving a typical load profile. Compressor type has a significant chiller performance impact. Performance of screw and reciprocating compressors is expressed in terms of pressure ratio and speed for a given refrigerant and suction density. Isentropic efficiency for a screw compressor is strongly affected by under- and over-compression (UOC) processes. The theoretical simple physical UOC model involves a compressor-specific (but sometimes unknown) volume index parameter and the real gas properties of the refrigerant used. Isentropic efficiency is estimated by the UOC model and a bi-cubic, used to account for flow, friction and electrical losses. The unknown volume index, a smoothing parameter (to flatten the UOC model peak) and bi-cubic coefficients are identified by curve fitting to minimize an appropriate residual norm. Chiller performance maps are produced for each compressor type by selecting optimized sub-cooling and condenser fan speed options in a generic component-based chiller model. SEER is the sum of hourly load (from a typical building in the climate of interest) and specific power for the same hourly conditions. An empirical UAE cooling load model, scalable to any equipment capacity, is used to establish proposed UAE MEPS. Annual electricity use and cost, determined from SEER and annual cooling load, and chiller component cost data are used to find optimal chiller designs and perform life-cycle cost comparison between screw and reciprocating compressor-based chillers. This process may be applied to any climate/load model in order to establish optimized MEPS for any country and/or region.

Numerical investigation on influence of real gas properties on nonlinear behavior of labyrinth seal-rotor system

A nonlinear model of fluid-structure interaction between high-pressure methane leakage through interlocking seal and the whirling rotor was proposed. The real gas properties of the methane at the pressure 102 bar were considered in the mathematical reduction. Three cases of different pressure ratio 1.7, 2.5 and 3.3 at the constant inlet pressure 250 bar were chosen in the present study. Two models, e.g., ideal gas model and real gas model, were employed to investigate the influence of real gas properties of methane leakage on the rotor dynamics. Distribution of thermal parameters in the seal cavities and seal clearance were determined, e.g., density, temperature, compressibility factor and specific heat capacity. The rotor-seal system was modeled as a Jeffcot rotor subject to shear stress and pressure force associated with the methane gas leakage. Spatio-temporal variation of the methane gas forcing on the rotor surface in the coverage of the seal clearance and the cavity volume was calculated by using the Muzynska model and the perturbation analysis, respectively. The governing equation of rotor dynamics which includes the main contribution from the methane leakage forcing was solved by using the fourth-order Runge–Kutta method, resulting in the orbit of the whirling rotor.

Surface roughness effect on flow measurement of real gas in a critical nozzle

Critical nozzles are widely used in the flow measurement. The discharge coefficient is the most important performance parameter of critical nozzle. At present, the critical nozzle has increasingly been applied in high-pressure and high Reynolds number flow. Thus, the effect of surface roughness on discharge coefficient should be noticed. The effects of relative equivalent sand roughness on discharge coefficient of real gas in a wide range of temperature and pressure were investigated. The thermodynamic properties and transport properties of real gas can be calculated by MBWR EoS, Helmholtz energy EoS and ECS real gas models. Standard k–ε model with the wall function was used to predict the discharge coefficient with good accuracy. Numerical results were validated by existing experimental data. The effect of roughness related with parametric Reynolds number, nozzle curvature radius and specific heat ratio were discussed in details. The roughness effect will become larger with the increase of all these parameters. At last, the roughness effects on discharge coefficient of real gas, such as argon, nitrogen and methane with a wide range of pressure while temperature ranges from 300K to 500K and Ks/d ranges from 10−2 to 10−5 were studied. All of results coincided well with previous parametric studies.

Thermodynamic properties of real gases and BWR equation of state

The fundamental base for the calculation of the thermodynamic properties of materials is thermal equation of state and dependence of some of the basic specific heat capacities on temperature. The dependence of the specific thermal capacity on the second independent variable (for example on the volume) it is already possible to deduce from the thermal equation of state. The aim of this paper is to assess the compliance values of specific heat capacity which was calculated using the BWR thermal equation of the state and experimentally obtained known values of specific heat capacity for the substance, whose characteristics are available in a wide range of state space.

Performance analysis of a supersonic ejector cycle working with R245fa

A supersonic ejector chiller for industrial use is currently being developed and tested as part of a project cooperation between Frigel s.p.a and DIEF (Department of Industrial Engineering, University of Florence). The refrigerator was built following a “ready to market” setup criterion and is intended for applications on the industrial refrigeration market or in air conditioning. The plant has a nominal cooling power of 40 kW and is powered by low temperature heat (from 90 up to 100 °C). The ejector is equipped with a movable primary nozzle and 9 static pressure probes along the mixing chamber/diffuser duct. The working fluid is R245fa. An extensive numerical campaign was performed to analyze the internal dynamics of the ejector. All the simulations were carried out by accounting for the real gas properties of the refrigerant. Comparison with experimental data resulted in close agreement both in terms of global and local parameters. Analyses showed that in order to achieve an accurate matching with the experimental data, it is necessary to correctly account for the surface roughness of the ejector. This is especially true for off-design operating conditions.