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

Water ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 530 ◽  
Author(s):  
Weixiang Ni ◽  
Jian Zhang ◽  
Lin Shi ◽  
Tengyue Wang ◽  
Xiaoying Zhang ◽  
...  
Keyword(s):  
Water Depth ◽  
Small Volume ◽  
Pressure Oscillation ◽  
State Equation ◽  
Ideal Gas ◽  
Pipeline System ◽  
Real Gas ◽  
Polytropic Equation ◽  
Real Gas Equations ◽  
Ideal Gas Model

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.

scholarly journals A Numerical Study on the Supersonic Steam Ejector Use in Steam Turbine System

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Lin Cai ◽  
Miao He
Keyword(s):  
Steam Turbine ◽  
Numerical Study ◽  
Fluid Pressure ◽  
Ideal Gas ◽  
Entrainment Ratio ◽  
Real Gas ◽  
Steam Ejector ◽  
Mixing Chamber ◽  
Cfd Method ◽  
Ideal Gas Model

Supersonic steam ejector is widely used in steam energy systems such as refrigeration, wood drying equipment, papermaking machine, and steam turbine. In this paper the Computational Fluids Dynamics (CFD) method was employed to simulate a supersonic steam ejector, SST k-w turbulence model was adopted, and both real gas model and ideal gas model for fluid property were considered and compared. The mixing chamber angle, throat length, and nozzle exit position (NXP) primary pressure and temperature effects on entrainment ratio were investigated. The results show that performance of the ejector is underestimated using ideal gas model, and the entrainment ratio is 20%–40% lower than that when using real gas model. There is an optimum mixing chamber angel and NXP makes the entrainment ratio achieve its maximum; as throat length is decreased within a range, the entrainment ratio remains unchanged. Primary fluid pressure has a critical value, and the entrainment ratio reaches its peak at working critical pressure; when working steam superheat degree increases, the entrainment ratio is increased.

Study on Mathematic Model of Air Valve Based on Real Gas Characteristics

2007 ◽  
Author(s):  
Jianyong Hu ◽  
Jian Zhang ◽  
Lisheng Suo ◽  
Yuan Zheng
Keyword(s):  
Water Supply ◽  
Mathematic Model ◽  
State Equation ◽  
Ideal Gas ◽  
Supply System ◽  
Protective Function ◽  
Real Gas ◽  
Air Inlet ◽  
Characteristics Method ◽  
Air Valve

Air valve is an important measure of water hammer protection in long water supply system. Accurate simulation of the air-inlet and air outlet process of air valve is directly relative to the safety of water supply engineering. Operational principle of air valve is analyzed and new mathematic model of air valve is built based on Van der Waals equation. Protective function of air valve in transient process caused by valve closing is analyzed with the characteristics method. The result shows the new mathematic model of air valve presents a series of new characteristics in the process of air-inlet and air-outlet comparing with the old mathematic model based on ideal-gas state equation.

Thermodynamic Property Models for Moist Air and Combustion Gases

2002 ◽  
Vol 125 (1) ◽  
pp. 374-384 ◽  
Author(s):  
D. Bu¨cker ◽  
R. Span ◽  
W. Wagner
Keyword(s):  
Ideal Gas ◽  
Moist Air ◽  
Combustion Gas ◽  
Real Gas ◽  
New Model ◽  
Combustion Gases ◽  
Dissociation Model ◽  
The Individual ◽  
Ideal Gas Model ◽  
The Ideal

A new model for the prediction of caloric properties of moist air and combustion gases has been developed. The model very accurately predicts ideal gas caloric properties of undissociated gas mixtures at temperatures from 200 K to 3300 K. In addition, a simple model has been developed to account for caloric effects of dissociation at temperatures up to 2000 K. As a part of the project, scientific equations for the ideal gas isobaric heat capacity of the individual combustion gas components have been established. Based on this reference, an assessment and comparison of the new model with the most common technical models have been carried out. Results of the simplified dissociation model are compared to the results of complex chemical equilibrium programs. To mark out the limits of the ideal gas hypothesis, some sample calculations are given, which compare results of the new ideal gas model to results from sophisticated real gas models.

AN APPLICATION OF NONEXTENSIVE PARAMETER: THE NONEXTENSIVE GAS AND REAL GAS

2007 ◽  
Vol 21 (06) ◽  
pp. 947-953 ◽  
Author(s):  
YAHUI ZHENG ◽  
JIULIN DU
Keyword(s):  
Heat Capacity ◽  
Second Virial Coefficient ◽  
Ideal Gas ◽  
Quasi Equilibrium ◽  
Equilibrium System ◽  
Real Gas ◽  
Nonextensive Statistics ◽  
Thomson Coefficient ◽  
Ideal Gas Model ◽  
The Ideal

By application of the nonextensive statistics to the ideal gas model, we establish a nonextensive gas model. If we regard the nonextensive gas as a real gas, we can use the nonextensive parameter q ∈ ℝ in Tsallis statistics to describe Joule coefficient, Joule–Thomson coefficient, second virial coefficient and etc. We also derive an expression, with a multiplier T1-q, of the heat capacity of the nonextensive gas. We can prove that in the quasi-equilibrium system there is 1 - q > 0, 2 so the heat capacity still vanishes if temperature tends to zero, just as that in Boltzmann-Gibbs statistics.

CFD-Simulation of Centrifugal Fan Performance Characteristics Using Ideal and Real Gas Models for Air and Organic Fluids

2019 ◽  
Author(s):  
Manuel Fritsche ◽  
Philipp Epple ◽  
Karsten Hasselmann ◽  
Felix Reinker ◽  
Robert Wagner ◽  
...  
Keyword(s):  
Cfd Simulation ◽  
Ideal Gas ◽  
High Tech ◽  
Test Case ◽  
Centrifugal Fan ◽  
Real Gas ◽  
The Real ◽  
Organic Fluids ◽  
Ideal Gas Model ◽  
The Ideal

Abstract Efficient processes with organic fluids are becoming increasingly important. The high tech fluid Novec™ is such an organic fluid and is used, for example, as a coolant for highperformance electronics, low-temperature heat transfer applications, cooling of automotive batteries, just to mention a few. Thus, efficient designed fans for the transport of organic fluids are becoming more and more important in the process engineering. CFD-simulations are nowadays integral part of the design and optimization process of fans. For air at the most usual application conditions, i.e. no extreme temperatures or pressures, the ideal gas model is in good agreement with the real gas approach. In the present study, this real gas approach for organic fluids have been investigated with CFD methods and, the deviation from the ideal gas model has been analyzed. For this purpose, a simulation model of a centrifugal fan with volute has been designed as a test case. First, the ideal gas model approach has been compared with the real gas approach model of Peng-Robinson for air using the commercial solver ANSYS CFX. Thereafter, the same comparison has been performed using the organic fluid Novec™. After a detailed grid study, the entire fan characteristics, i.e. the design point and the off-design points, have been simulated and evaluated for each fluid (air and Novec™) and gas model (ideal gas and Peng-Robinson real gas). The steady state simulations of the centrifugal fan have been performed using the Frozen Rotor model. The simulation results have been compared, discussed and presented in detail.

Uncertainty Analysis of a Polytropic Compression Process and Application to Centrifugal Compressor Performance Testing

2005 ◽  
Author(s):  
Jose´ L. Gilarranz
Keyword(s):  
Uncertainty Analysis ◽  
Centrifugal Compressor ◽  
Equations Of State ◽  
Pressure Ratio ◽  
Ideal Gas ◽  
Isentropic Compression ◽  
Real Gas ◽  
Compression Model ◽  
Test Loop ◽  
Real Gas Equations

In recent years, several papers have been written concerning the application of uncertainty analyses for isentropic compression processes under the assumption of ideal gas behavior. However, for high-pressure ratio machines, the ideal gas model fails to capture the physics of the process. Still, the estimation of test uncertainty for polytropic processes is hindered by the complexity of the equations used to calculate the performance parameters and by the incorporation of real gas equations into the models. This paper presents an uncertainty analysis developed to estimate the error levels in data gathered during factory aero-performance tests of single- or multi-stage centrifugal compressors. The analysis incorporates the effects of the variation and uncertainty levels of every parameter used to calculate centrifugal compressor aero-thermal performance. Included are the variables used to define the thermodynamic states of the fluid inside the compressor, as well as geometric and operational parameters associated with the machine and test loop. Two different methods have been utilized and the results compared to evaluate the advantages and drawbacks of each. The first method is based on the direct use of the Monte Carlo simulation technique combined with real gas equations of state. The second method employs uncertainty propagation equations and the methodology included in the ASME PTC-19.1 (1998) Test Code. Both approaches utilize the polytropic compression model and equations for performance evaluation that are included in the ASME PTC 10 (1997) Power Test Code for compressors and exhausters. The methods and results from this work may be easily extended to the isentropic compression model as well. The use of real gas equations of state make the methods applicable to virtually any gas composition. Although the analysis was intended to be applied to ASME PTC 10 Type 2 tests, the method can be extended to evaluate Type 1 and/or on-site field tests, as long as certain considerations are addressed. The uncertainty analysis presented is then used to evaluate data from several machines, ranging from a low-pressure ratio gas pipeline compressor to an eight-stage machine used for natural gas processing. Comments are offered concerning the effects of machine pressure ratio on the levels of uncertainty, as well as the importance of proper selection of instrumentation to minimize the error level of the test data. Special emphasis is placed on the benefits of using this analysis during the planning phase of the test program, to determine the optimal combination of instruments, to guarantee acceptable levels of uncertainty.

scholarly journals Real Gas Models in Coupled Algorithms Numerical Recipes and Thermophysical Relations

2020 ◽  
Vol 5 (3) ◽  
pp. 20
Author(s):  
Lucian Hanimann ◽  
Luca Mangani ◽  
Ernesto Casartelli ◽  
Damian Vogt ◽  
Marwan Darwish
Keyword(s):  
Gas Flow ◽  
Measurement Data ◽  
Ideal Gas ◽  
Computational Time ◽  
State Equations ◽  
Cfd Simulations ◽  
Real Gas ◽  
Standard Ideal ◽  
Ideal Gas Model ◽  
The Ideal

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.

The Effect of Gas Models on Compressor Efficiency Including Uncertainty

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
Fangyuan Lou ◽  
John Fabian ◽  
Nicole L. Key
Keyword(s):  
Pressure Ratio ◽  
Ideal Gas ◽  
Experimental Measurements ◽  
Perfect Gas ◽  
Real Gas ◽  
The Real ◽  
Compressor Efficiency ◽  
Ideal Gas Model ◽  
Isentropic Efficiency ◽  
The Ideal

Since isentropic efficiency is widely used in evaluating the performance of compressors, it is essential to accurately calculate this parameter from experimental measurements. Quantifying realistic bounds of uncertainty in experimental measurements are necessary to make meaningful comparisons to computational fluid dynamics simulations. This paper explores how the gas model utilized for air can impact not only the efficiency calculated in an experiment, but also the uncertainty associated with that calculation. In this paper, three different gas models are utilized: the perfect gas model, the ideal gas model, and the real gas model. A commonly employed assumption in calculating compressor efficiency is the perfect gas assumption, in which the specific heat, is treated as a constant and is independent of temperature and pressure. Results show significant differences in both calculated efficiency and the resulting uncertainty in efficiency between the perfect gas model and the real gas model. The calculated compressor efficiency from the perfect gas model is overestimated, while the resulting uncertainties from the perfect gas model are underestimated. The ideal gas model agrees well with the real gas model, however. Including the effect of uncertainty in gas properties results in very large uncertainties in isentropic efficiency, on the order of ten points, for low pressure ratio machines.

Computational fluid dynamics simulation of the supersonic steam ejector. Part 1: Comparative study of different equations of state

2011 ◽  
Vol 226 (3) ◽  
pp. 709-714 ◽  
Author(s):  
H T Zheng ◽  
L Cai ◽  
Y J Li ◽  
Z M Li
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Flow Field ◽  
Equations Of State ◽  
Ideal Gas ◽  
Dynamics Simulation ◽  
Real Gas ◽  
Steam Ejector ◽  
Ideal Gas Model ◽  
The Ideal

The aim of this study is to investigate the use of computational fluid dynamics in predicting the performance and geometry of the optimal design of a steam ejector used in a steam turbine. Many scholars have analysed the steam ejector using the ideal gas model, which lacks accuracy in terms of calculating the flow field of the ejector. This study is reported in a series of two papers. The first part covers the validation of CFX 11.0 results using different equations of state (EOS) on the converging–diverging nozzle flow field carried out with the experimental value. The IAPWS IF97 real gas model works well with the experimental value. The flow field of the ejector was analysed using different EOS after grid-dependent learning. The results show that the performance of the ejector was underestimated under the ideal gas model; the entrainment ratio was 20–40 per cent lower than when using the real gas model. The effect of the optimal geometrical design and operating conditions will be discussed in Part 2.

scholarly journals High-intensity air-explosion-induced shock loading of structures: consideration of a real gas in modelling a nonlinear compressible medium

2015 ◽  
Vol 471 (2176) ◽  
pp. 20140825 ◽  
Author(s):  
R. Ghoshal ◽  
N. Mitra
Keyword(s):  
High Intensity ◽  
Intermolecular Forces ◽  
Ideal Gas ◽  
Compressible Medium ◽  
Light Weight ◽  
Air Blast ◽  
Real Gas ◽  
The Real ◽  
Ideal Gas Model ◽  
The Ideal

The existing practice of designing air-blast-resistant structures relies on the ideal gas model. But this model predicts the maximum value of the reflection coefficient (ratio of the reflected to the incident pressure) to be 8, whereas it can go up to 20 or more as reported in the literature. To address this discrepancy, air medium is modelled as a real gas instead of an ideal gas, where the effect of intermolecular forces, vibration, dissociation, electronic excitation and ionization are included. Ranges of peak over-pressure are identified where the ideal gas assumption cannot be used. Differences in impulse transmitted to the free-standing plates of different mass owing to relaxing of the ideal gas assumption and consideration of the real gas model are evaluated. Impulse transmitted to the structures for constant and variable back pressure (VBP) is also compared considering the real gas model. The result shows that for high-intensity shock, the ideal gas model under-predicts impulse transmitted to heavy plates but over-predicts the same for light-weight plates. Impulse transmitted to light-weight plates is also overestimated if VBP is neglected. The implications of this research are substantial for designing high-intensity air-blast mitigating structures, which if not considered properly, may lead to compromise in structural performance.

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