The Influence of Real Gas Properties on Predictions of Static and Rotordynamic Properties of Annular Seals for Injection Compressors

2007 ◽  
Author(s):  
Yoon-Shik Shin ◽  
Dara W. Childs
Keyword(s):  
Energy Equation ◽  
Control Volume ◽  
Ideal Gas ◽  
Running Speed ◽  
Real Gas ◽  
Adiabatic Flow ◽  
Rotordynamic Coefficients ◽  
Ideal Gas Law ◽  
Piston Seal ◽  
Gas Properties

Predictions are presented for an annular gas seal that is representative of the division-wall seal of a back-to-back compressor or the balance-piston seal of an in-line compressor. A 2-control-volume bulk-flow model is used including the axial and circumferential momentum equations and the continuity equations. The basic model uses a constant temperature prediction (ISOT) and an ideal gas law as an equation of state. Two variations are used: adding the energy equation with an ideal gas law (IDEAL), and adding the energy equation with real gas properties (REAL). The energy equations assume adiabatic flow. The ISOT model has been used for prior calculations. Concerning predictions of static characteristics, the calculated mass leakage rate was, respectively, 9.46, 9.55 and 7.87 kg/s for ISOT, IDEAL, and REAL. For rotordynamic coefficients, predicted effective stiffness coefficients are comparable for the models at low excitation frequencies. At running speed, REAL predictions are roughly 40% lower than ISOT, which could results in lower predicted critical speeds. Predicted effective damping coefficients are also generally comparable. REAL and IDEAL predictions for the cross-over frequency is approximately 20% lower than ISOT. REAL predictions for effective damping are modestly lower in the frequency range of 40 to 50% of running speed where higher damping values are desired.

The Impact of Real Gas Properties on Predictions of Static and Rotordynamic Properties of the Annular Gas Seals for Injection Compressors

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Yoon-Shik Shin ◽  
Dara W. Childs
Keyword(s):  
Energy Equation ◽  
Control Volume ◽  
Ideal Gas ◽  
Running Speed ◽  
Real Gas ◽  
Ideal Gas Law ◽  
Piston Seal ◽  
Gas Seals ◽  
The Impact ◽  
Gas Properties

Predictions are presented for an annular gas seal that is representative of the division-wall seal of a back-to-back compressor or the balance-piston seal of an in-line compressor. A two-control-volume bulk-flow model is used including the axial and circumferential momentum equations and the continuity equations. The basic model uses a constant-temperature prediction (ISOT) and an ideal gas law as an equation of state. Two variations are used: adding the energy equation with an ideal gas law (IDEAL), and adding the energy equation with real gas properties (REAL). The energy equations assume adiabatic flow. The ISOT model has been used for prior calculations. Concerning predictions of static characteristics, the calculated mass leakage rates were, respectively, 9.46 kg∕s, 9.55 kg∕s, and 7.87 kg∕s for ISOT, IDEAL, and REAL. For rotordynamic coefficients, predicted effective stiffness coefficients are comparable for the models at low excitation frequencies. At running speed, REAL predictions are roughly 40% lower than ISOT, which could result in lower predicted critical speeds. Predicted effective damping coefficients are also generally comparable. REAL and IDEAL predictions for the crossover frequency are approximately 20% lower than ISOT. REAL predictions for effective damping are modestly lower in the frequency range of 40–50% of running speed where higher damping values are desired.

Measurement Versus Predictions of Rotordynamic Coefficients of a Hole-Pattern Gas Seal With Negative Preswirl

2012 ◽  
Vol 134 (12) ◽  
Author(s):  
Philip D. Brown ◽  
Dara W. Childs
Keyword(s):  
Control Volume ◽  
Pressure Ratio ◽  
Excitation Frequency ◽  
Ideal Gas ◽  
Crossover Frequency ◽  
Rotor Speed ◽  
Rotordynamic Coefficients ◽  
Damping Coefficients ◽  
Ideal Gas Law ◽  
Stiffness And Damping

Test results are presented for the rotordynamic coefficients of a hole-pattern annular gas seal at supply pressures to 84 bar and running speeds to 20200 rpm. The principal test variable of interest was negative preswirl. Preswirl signifies the circumferential fluid flow entering a seal and negative preswirl indicates a fluid swirl in a direction opposite to rotor rotation. The influences of the pressure ratio and rotor speed were also investigated. The measured results produce direct and cross-coupled stiffness and damping coefficients that are a function of the excitation frequency Ω. Changes in the pressure ratio had only small effects on most rotordynamic coefficients. Cross-coupled stiffness showed slightly different profiles through the midrange of Ω values. Increasing rotor speed significantly increased the cross-coupled stiffness and cross-coupled damping. At 10,200 RPM, high negative inlet preswirl produced negative cross-coupled stiffness over an excitation frequency range of 200–250 Hz. Negative preswirl did not affect the direct stiffness and damping coefficients. Effective damping combines the stabilizing effect of direct damping and the destabilizing effect of cross-coupled stiffness. The crossover frequency is the precession frequency where effective damping transitions from a negative value to a positive value with increasing frequency. At 20,200 rpm with a pressure ratio of 50%, the peak effective damping was increased by 50%, and the crossover frequency was reduced by 50% for high-negative preswirl versus zero preswirl. Hence, reverse swirl can greatly enhance the stabilizing capacity of a hole-pattern balance-piston or division-wall seals for compressors. A two-control-volume model that uses the ideal gas law at constant temperature was used to predict rotordynamic coefficients. The model predicted direct rotordynamic coefficients well, however, substantially under-predicted cross-coupled rotordynamic coefficients, especially at high negative preswirls.

Measurement Versus Predictions of Rotordynamic Coefficients of a Hole-Pattern Gas Seal With Negative Preswirl

2012 ◽  
Author(s):  
Philip D. Brown ◽  
Dara W. Childs
Keyword(s):  
Control Volume ◽  
Pressure Ratio ◽  
Excitation Frequency ◽  
Ideal Gas ◽  
Rotor Speed ◽  
Rotordynamic Coefficients ◽  
Damping Coefficients ◽  
The Cross ◽  
Gas Seals ◽  
Stiffness And Damping

Test results are presented for rotordynamic coefficients of a hole-pattern annular gas seals at supply pressures to 84 bar and running speeds to 20,200 RPM. The principal test variable of interest was negative preswirl. Preswirl signifies the circumferential fluid flow entering a seal, and negative preswirl indicates a fluid swirl in a direction opposite to rotor rotation. The influences of pressure ratio and rotor speed were also investigated. Measured results produce direct and cross-coupled stiffness and damping coefficients that are a function of excitation frequency Ω. Changes in pressure ratio had only small effects on most rotordynamic coefficients. Cross-coupled stiffness showed slightly different profiles through the mid-range of Ω values. Increasing rotor speed significantly increased cross-coupled stiffness and cross-coupled damping. At 10,200 RPM, high negative inlet preswirl produced negative cross-coupled stiffness over an excitation frequency range of 200–250 Hz. Negative preswirl did not affect direct stiffness and damping coefficients. Effective damping combines the stabilizing effect of direct damping and the destabilizing effect of cross-coupled stiffness. The cross-over frequency is the precession frequency where effective damping transitions from a negative value to a positive value with increasing frequency. At 20,200 RPM with a pressure ratio of 50%, peak effective damping was increased by 50%, and the cross-over frequency was reduced by 50% for high-negative preswirl versus zero preswirl. Hence, reverse swirl can greatly enhance the stabilizing capacity of hole-pattern balance-piston or division-wall seals for compressors. A two-control-volume model that uses the ideal gas law at constant temperature was used to predict rotordynamic coefficients. The model predicted direct rotordynamic coefficients well, but substantially under predicted cross-coupled rotordynamic coefficients especially at high negative preswirls.

Numerical Simulation of Steam Flow Inside the Superheater Section of An Industrial Boiler Using a Real Gas Model

2020 ◽  
Vol 142 (7) ◽  
Author(s):  
Deepak Kumar Kanungo ◽  
Kirti Chandra Sahu
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Supercritical Fluids ◽  
Ideal Gas ◽  
Real Gas ◽  
Absolute Value ◽  
Ideal Gas Law ◽  
Maximum Value ◽  
Industrial Boiler ◽  
The Ideal

Abstract Flow mal-distribution inside manifolds hampers the overall efficiency of processes in industries. In supercritical boilers, improper flow of steam inside the superheater (SH) section is a common cause of thermal accidents. However, carrying out a numerical simulation of supercritical fluids flowing inside manifolds is challenging as the ideal gas law does not describe the behavior of these fluids properly. In the present work, numerical simulation of the flow of supercritical steam inside the superheater section of an industrial boiler has been performed using a real gas model. The proposed real gas model is first validated with experimental data associated with the steam properties. Subsequently, the effect of different inlet and outlet arrangements on the flow mal-distribution of steam in the superheater section of the boiler is investigated numerically using the real gas model. A modified inlet and outlet arrangement of the superheater header is proposed which reduces the maximum value of flow mal-distribution in the header by 19.7% and total pressure drop in the domain by 17%. The effect of the Reynolds number on flow mal-distribution in the header arrangement is found to be negligible. The absolute value of the heat absorption by the superheater tubes increases with an increase in the value of the Reynolds number.

The Use of Real Gas Properties for Design and Flow Field Simulations of a Small Centripetal Steam Turbine

2009 ◽  
Author(s):  
Jianjun Feng ◽  
Friedrich-Karl Benra ◽  
Hans Josef Dohmen
Keyword(s):  
Steam Turbine ◽  
Design Procedure ◽  
Flow Fields ◽  
Ideal Gas ◽  
Real Gas ◽  
The Real ◽  
Real Gas Effects ◽  
Applied Design ◽  
Small Capacity ◽  
Gas Properties

In this paper, the applied design procedure for generation of a small-capacity ORC centripetal steam turbine working with the fluid 1, 1, 1, 3, 3-Pentafluoropropane (R245fa) is described with consideration of real gas effects. After specification of the turbine geometry in an iterative process using different commercial design tools which have been enhanced in order to work with real gas conditions, CFD simulations based on the real gas properties of the fluid have been conducted for the originated geometry. The simulations are performed by using the CFD code ANSYS-CFX11 with a pre-prepared real gas property (RGP) table, which comprises the required gas properties at different discrete pressure and temperature values. In addition, the flow fields inside the turbine obtained from the real gas model is compared to those flow fields which are obtained by the ideal gas model and also by the Redlich-Kwong model.

Making sense of sensemaking: using the sensemaking epistemic game to investigate student discourse during a collaborative gas law activity

2021 ◽  
Author(s):  
Kevin H. Hunter ◽  
Jon-Marc G. Rodriguez ◽  
Nicole M. Becker
Keyword(s):  
Problem Solving ◽  
Conceptual Understanding ◽  
Ideal Gas ◽  
Interactive Simulation ◽  
Structural Components ◽  
Student Discourse ◽  
Coding Scheme ◽  
Making Sense ◽  
Ideal Gas Law ◽  
The Ideal

Beyond students’ ability to manipulate variables and solve problems, chemistry instructors are also interested in students developing a deeper conceptual understanding of chemistry, that is, engaging in the process of sensemaking. The concept of sensemaking transcends problem-solving and focuses on students recognizing a gap in knowledge and working to construct an explanation that resolves this gap, leading them to “make sense” of a concept. Here, we focus on adapting and applying sensemaking as a framework to analyze three groups of students working through a collaborative gas law activity. The activity was designed around the learning cycle to aid students in constructing the ideal gas law using an interactive simulation. For this analysis, we characterized student discourse using the structural components of the sensemaking epistemic game using a deductive coding scheme. Next, we further analyzed students’ epistemic form by assessing features of the activity and student discourse related to sensemaking: whether the question was framed in a real-world context, the extent of student engagement in robust explanation building, and analysis of written scientific explanations. Our work provides further insight regarding the application and use of the sensemaking framework for analyzing students’ problem solving by providing a framework for inferring the depth with which students engage in the process of sensemaking.

A Complete Solution for Thermal-Elastohydrodynamic Lubrication of Line Contacts Using Circular Non-Newtonian Fluid Model

1992 ◽  
Vol 114 (3) ◽  
pp. 540-551 ◽  
Author(s):  
Hsing-Sen S. Hsiao ◽  
Bernard J. Hamrock
Keyword(s):  
Boundary Conditions ◽  
Newtonian Fluid ◽  
Energy Equation ◽  
Control Volume ◽  
Fluid Model ◽  
Complete Solution ◽  
Circular Model ◽  
Line Contacts ◽  
Stress Boundary Conditions ◽  
Stress Boundary

A complete solution is obtained for elastohydrodynamically lubricated conjunctions in line contacts considering the effects of temperature and the non-Newtonian characteristics of lubricants with limiting shear strength. The complete fast approach is used to solve the thermal Reynolds equation by using the complete circular non-Newtonian fluid model and considering both velocity and stress boundary conditions. The reason and the occasion to incorporate stress boundary conditions for the circular model are discussed. A conservative form of the energy equation is developed by using the finite control volume approach. Analytical solutions for solid surface temperatures that consider two-dimensional heat flow within the solids are used. A straightforward finite difference method, successive over-relaxation by lines, is employed to solve the energy equation. Results of thermal effects on film shape, pressure profile, streamlines, and friction coefficient are presented.

Impact of Frequency Dependence of Gas Labyrinth Seal Rotordynamic Coefficients on Centrifugal Compressor Stability

2010 ◽  
Author(s):  
Giuseppe Vannini ◽  
Manish R. Thorat ◽  
Dara W. Childs ◽  
Mirko Libraschi
Keyword(s):  
Molecular Weight ◽  
Numerical Model ◽  
Control Volume ◽  
Labyrinth Seal ◽  
Labyrinth Seals ◽  
Frequency Dependent ◽  
Rotordynamic Coefficients ◽  
Frequency Independent ◽  
Rotor Surface ◽  
Independent Model

A numerical model developed by Thorat & Childs [1] has indicated that the conventional frequency independent model for labyrinth seals is invalid for rotor surface velocities reaching a significant fraction of Mach 1. A theoretical one-control-volume (1CV) model based on a leakage equation that yields a reasonably good comparison with experimental results is considered in the present analysis. The numerical model yields frequency-dependent rotordynamic coefficients for the seal. Three real centrifugal compressors are analyzed to compare stability predictions with and without frequency-dependent labyrinth seal model. Three different compressor services are selected to have a comprehensive scenario in terms of pressure and molecular weight (MW). The molecular weight is very important for Mach number calculation and consequently for the frequency dependent nature of the coefficients. A hydrogen recycle application with MW around 8, a natural gas application with MW around 18, and finally a propane application with molecular weight around 44 are selected for this comparison. Useful indications on the applicability range of frequency dependent coefficients are given.

A Comparison of Rotordynamic-Coefficient Predictions for Annular Honeycomb Gas Seals Using Three Different Friction-Factor Models

2002 ◽  
Vol 124 (3) ◽  
pp. 524-529 ◽  
Author(s):  
Rohan J. D’Souza ◽  
Dara W. Childs
Keyword(s):  
Friction Factor ◽  
Flow Model ◽  
Factor Model ◽  
Control Volume ◽  
Bulk Flow ◽  
Shear Stresses ◽  
Steam Turbines ◽  
Frequency Range ◽  
Rotordynamic Coefficients ◽  
Rotordynamic Coefficient

A two-control-volume bulk-flow model is used to predict rotordynamic coefficients for an annular, honeycomb-stator/smooth-rotor gas seal. The bulk-flow model uses Hirs’ turbulent-lubrication model, which requires a friction factor model to define the shear stresses at the rotor and stator wall. Rotordynamic coefficients predictions are compared for the following three variations of the Blasius pipe-friction model: (i) a basic model where the Reynolds number is a linear function of the local clearance, fs=ns Rems (ii) a model where the coefficient is a function of the local clearance, and (iii) a model where both the coefficient and exponent are functions of the local clearance. The latter models are based on data that shows the friction factor increasing with increasing clearances. Rotordynamic-coefficient predictions shows that the friction-factor-model choice is important in predicting the effective-damping coefficients at a lower frequency range (60∼70 Hz) where industrial centrifugal compressors and steam turbines tend to become unstable. At a higher frequency range, irrespective of the friction-factor model, the rotordynamic-coefficient predictions tend to coincide. Blasius-based Models which directly account for the observed increase in stator friction factors with increasing clearance predict significantly lower values for the destabilizing cross-coupled stiffness coefficients.

scholarly journals Thermodynamic Analysis of Irreversible Desiccant Systems

Entropy ◽  
2018 ◽  
Vol 20 (8) ◽  
pp. 595 ◽  
Author(s):  
Niccolò Giannetti ◽  
Seiichi Yamaguchi ◽  
Andrea Rocchetti ◽  
Kiyoshi Saito
Keyword(s):  
Control Volume ◽  
Ideal Gas ◽  
Maximum Efficiency ◽  
Working Fluid ◽  
Specific System ◽  
Equilibrium Relationship ◽  
Working Medium ◽  
Vapour Mixture ◽  
Energy Balances ◽  
Relationship Of

A new general thermodynamic mapping of desiccant systems’ performance is conducted to estimate the potentiality and determine the proper application field of the technology. This targets certain room conditions and given outdoor temperature and humidity prior to the selection of the specific desiccant material and technical details of the system configuration. This allows the choice of the operative state of the system to be independent from the limitations of the specific design and working fluid. An expression of the entropy balance suitable for describing the operability of a desiccant system at steady state is obtained by applying a control volume approach, defining sensible and latent effectiveness parameters, and assuming ideal gas behaviour of the air-vapour mixture. This formulation, together with mass and energy balances, is used to conduct a general screening of the system performance. The theoretical advantage and limitation of desiccant dehumidification air conditioning, maximum efficiency for given conditions constraints, least irreversible configuration for a given operative target, and characteristics of the system for a target efficiency can be obtained from this thermodynamic mapping. Once the thermo-physical properties and the thermodynamic equilibrium relationship of the liquid desiccant mixture or solid coating material are known, this method can be applied to a specific technical case to select the most appropriate working medium and guide the specific system design to achieve the target performance.

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