Mathematical Analysis for Off-Design Performance of Cryogenic Turboexpander

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
Subrata K. Ghosh ◽  
R. K. Sahoo ◽  
Sunil K. Sarangi
Keyword(s):  
Pressure Ratio ◽  
Expansion Ratio ◽  
Flow Conditions ◽  
Flow Properties ◽  
Dimensional Solution ◽  
One Dimensional ◽  
Design Performance ◽  
Fluid Properties ◽  
The Mean ◽  
Inlet Conditions

A study has been conducted to determine the off-design performance of cryogenic turboexpander. A theoretical model to predict the losses in the components of the turboexpander along the fluid flow path has been developed. The model uses a one-dimensional solution of flow conditions through the turbine along the mean streamline. In this analysis, the changes of fluid and flow properties between different components of turboexpander have been considered. Overall, turbine geometry, pressure ratio, and mass flow rate are input information. The output includes performance and velocity diagram parameters for any number of given speeds over a range of turbine pressure ratio. The procedure allows any arbitrary combination of fluid species, inlet conditions, and expansion ratio since the fluid properties are properly taken care of in the relevant equations. The computational process is illustrated with an example.

Radial Inlet and Exit Off-Design Performance Prediction for a 10 MWe Supercritical CO2 Axial Turbine

2021 ◽  
Author(s):  
Michael Marshall ◽  
Thomas Vandeputte ◽  
Stefan Cich ◽  
Megan Herrara
Keyword(s):  
Cfd Simulation ◽  
Dynamic Pressure ◽  
Pressure Ratio ◽  
Step Cycle ◽  
Modeling Tools ◽  
Design Performance ◽  
Design Values ◽  
Inlet Conditions ◽  
Operating Points ◽  
Best Fit

Abstract During the development of a sCO2 turbine for the STEP program under DOE funding, radial inlet and exit designs were completed under mechanical and thermal constraints while seeking to maximize aerodynamic performance [1]. The flow path geometries of the designs were optimized at a single steady-state, design condition to minimize the total pressure loss. In order to efficiently characterize changes in performance across a range of operating points of the closed-loop cycle, off-design loss models for the inlet and exit diffuser have been created from CFD simulation results. To generate boundary conditions for the exit diffuser, numerous 1D exit profiles were selected from a regression analysis of turbine map points as a function of pressure ratio and corrected speed; radial inlet conditions emanated from planned cycle operating points. From base equation forms that include dynamic pressure and swirl components, equation constants were optimized to provide a best fit to CFD results. The equations generated were able to be integrated into existing STEP cycle modeling tools to enhance the prediction of turbine response as the operating point deviates significantly from design values. The methods outlined in this paper can provide a guide for evaluating the off-design performance of turbine inlet and exit designs dissimilar from conventional designs for which correlations are available.

Spontaneous Displacement of Resident Fluid in Heterogeneous Porous Medium

2018 ◽  
Author(s):  
Shabina Ashraf ◽  
Jyoti Phirani
Keyword(s):  
Porous Medium ◽  
Flow Behavior ◽  
Spontaneous Imbibition ◽  
Flow Properties ◽  
Heterogeneous Porous Medium ◽  
Lab On Chip ◽  
One Dimensional ◽  
Diffusive Dynamics ◽  
Fluid Properties ◽  
Homogeneous Porous Medium

Surface tension driven flow in which one fluid displaces another is of importance in microfluidic devices for diagnostics, lab on chip devices and flow in oil reservoirs. Spontaneous impregnation of a preferentially wetting phase displacing an existing non-wetting phase in a homogeneous porous medium is known to follow diffusive dynamics. However, in a heterogeneous porous medium the hydrodynamic interaction between the narrow and the wide pores significantly alters the impregnation behavior. Previous studies have shown that the imbibing fluid interface leads in the narrow pores contrary to the predictions from the diffusive dynamics of homogeneous porous medium. This is due to the higher suction pressure in the narrow pores which draw fluid from the wide pores. The effect of fluid properties and relative flow properties of the pores with respect to other pores on the non-wetting fluid displacement in the heterogeneous porous medium is still unknown. In the current work, we develop a quasi one-dimensional, lubrication approximation model, which predicts the spontaneous imbibition in a heterogeneous porous medium. We explore all the possible relative fluid properties and flow properties of the layers in the heterogeneous porous medium and show that our model is able to predict the flow behavior in all the cases. We also present the results of the spontaneous imbibition experiments, which agree with our model. The experiments show that the two phase interface progresses faster in the narrow pores as predicted by the one-dimensional model. The result is important for predicting and controlling the flow behavior in a heterogeneous porous medium.

Sizing Safety Valve Vent Pipes for Saturated Steam

1982 ◽  
Vol 104 (1) ◽  
pp. 247-251
Author(s):  
H. E. Brandmaier
Keyword(s):  
Ideal Gas ◽  
Gas Analysis ◽  
Saturated Steam ◽  
Flow Conditions ◽  
Flow Properties ◽  
Pipe Length ◽  
One Dimensional ◽  
Choked Flow ◽  
Pipe Outlet ◽  
Orifice Valve

An earlier one-dimensional ideal gas analysis was changed to incorporate equilibrium properties of steam as given by the 1967 ASME steam tables. A generalized procedure based on pressure and entropy as independent variables is used to calculate choked flow conditions at the valve orifice, valve pipe outlet and vent pipe outlet. At the third location, the results are independent of whether flow in the vent pipe is supersonic or subsonic. An integral method is used to calculate the vent pipe length required to choke the flow. Computed data are compared with ideal gas data. The vent pipe size, to prevent blowback into the powerplant, is less conservative using real steam data. The flow properties, particularly specific volume, are significantly different.

An Evaluation of 1D Design Methods for the Off-Design Performance Prediction of Automotive Turbocharger Compressors

2012 ◽  
Author(s):  
Peter Harley ◽  
Stephen Spence ◽  
Dietmar Filsinger ◽  
Michael Dietrich ◽  
Juliana Early
Keyword(s):  
Statistical Method ◽  
Empirical Data ◽  
Pressure Ratio ◽  
Design Methods ◽  
One Dimensional ◽  
Design Performance ◽  
Hot Gas ◽  
Further Development ◽  
Insight Into ◽  
Modelling Approach

Several one-dimensional design methods have been used to predict the off-design performance of three modern centrifugal compressors for automotive turbocharging. The three methods used are single-zone, two-zone, and a more recent statistical method. The predicted results from each method are compared against empirical data taken from standard hot gas stand tests for each turbocharger. Each of the automotive turbochargers considered in this study have notably different geometries and are of varying application. Due to the non-adiabatic test conditions, the empirical data has been corrected for the effect of heat transfer to ensure comparability with the 1D models. Each method is evaluated for usability and accuracy in both pressure ratio and efficiency prediction. The paper presents an insight into the limitations of each of these models when applied to one-dimensional automotive turbocharger design, and proposes that a corrected single-zone modelling approach has the greatest potential for further development, whilst the statistical method could be immediately introduced to a design process where design variations are limited.

ALGOR Gas Turbine Performance Modular Tool: One Dimensional Turbine Module Validation

2016 ◽  
Author(s):  
Stefano Piola ◽  
Roberto Canepa ◽  
Andrea Silingardi ◽  
Stefano Cecchi ◽  
Carlo Carcasci ◽  
...  
Keyword(s):  
Gas Turbine ◽  
Pressure Ratio ◽  
Operating Conditions ◽  
Computational Time ◽  
Flow Angle ◽  
One Dimensional ◽  
Design Performance ◽  
Turbine Performance ◽  
Air System ◽  
Secondary Air

One dimensional codes play a key role in gas turbine performance simulation: once they are calibrated they can give reliable results within very short computational time if compared to two or three dimensional analysis. Thanks to their ability to quickly evaluate flow, pressure and temperature along the energy conversion from fluid to shaft or reverse, one dimensional tools fit the requirements of modular-structured program for the simulation of complete gas turbine. In ASEN experience, ALGOR heat and mass balance software is used as a platform for system integration between each disciplines by means of a modular structure in which a large number of modules, chosen from the available library, are freely connected allowing to potentially analyze any gas turbine engine configuration. ALGOR code provides advanced cycle calculation capabilities for example in case that cooling and secondary air system layout modification have to be considered in design process. In these situations, a turbine map-based approach is hardly applicable, while a one dimensional aerodynamic row by row simulation can provide a suitable method for off-design turbine behavior prediction. In ASEN practice, ALGOR turbine module is calibrated at design point on one dimensional data provided by turbine designers and is then adopted for the engine configuration optimization or off-design performance evaluation. This paper presents the validation of the off-design performance prediction given by the ALGOR embedded 1D turbine model comparing calculated results with experimental ones. The warm air full scale test rig investigated within the GE-NASA “Energy Efficient Engine” program for the aerodynamic evaluation of a two stages high pressure turbine has been chosen as validation case. It includes both experimental performance maps varying turbine operating conditions such as speed and pressure ratio extending to the sub-idle and starting region and an analysis of cooling flow variation effect on turbine performance. Literature available loss and exit flow angle correlations are implemented and compared to experimental data. The results given by each of them are analyzed to appreciate their accuracy in evaluating efficiency and flow variations. In addition the paper shows the ability of the 1D turbine module to consider secondary air system modification impact on performance comparing calculated results to experimental ones. Literature correlations tuning on proprietary experimental results could further improve the tool performance for the off-design evaluation of ASEN turbine geometries.

Development of Method and Computer Program for Multistage Axial Compressor Design: Part II — Two-Dimensional Design and Validation Using CFD

2018 ◽  
Author(s):  
Milan Banjac ◽  
Milan V. Petrovic
Keyword(s):  
Computer Program ◽  
Pressure Ratio ◽  
Axial Compressor ◽  
Two Dimensional ◽  
Dimensional Solution ◽  
Initial Flow ◽  
One Dimensional ◽  
Compressor Design ◽  
Two Dimensional Flow ◽  
Line Design

Part I of this paper presents a method and a computer program for the mean design of multistage axial compressors. This second part describes a method and an additional computer routine that use the basic mean line design to create a fully two-dimensional flow solution and a compressor design. The two-dimensional solution according to a selected swirl vortex function is calculated using streamline curvature throughflow equations and spanwise distribution of losses. An iterative calculation procedure slightly reshapes the initial flow path in order to retain the desired input flow coefficients. Other variables such as stage loading parameters are changed in order to obtain the desired overall pressure ratio. A spanwise distribution of certain stage parameters can then be adjusted to achieve desired radial flow field variations. The basic one-dimensional input data can be varied at any moment to obtain a new one-dimensional result and the corresponding two-dimensional solution. A new output is created instantaneously and can be used for further CFD analysis, external throughflow, blade-to-blade flow computations or mechanical and vibration analysis.

Subsonic Adiabatic Flow in a Duct of Constant Cross-Sectional Area

1964 ◽  
Vol 68 (638) ◽  
pp. 117-126 ◽  
Author(s):  
A. J. Ward Smith
Keyword(s):  
Flow Theory ◽  
Flow Conditions ◽  
Mean Flow ◽  
Flow Properties ◽  
Cross Sectional ◽  
Fully Developed Flow ◽  
One Dimensional ◽  
Dimensional Flow ◽  
Loss Coefficients ◽  
The One

SummaryStarting from the momentum integral equation an analysis is made of fully-developed flow in a straight pipe. This analysis shows the assumptions implicit in the one-dimensional theory of adiabatic constant-area flow with friction. For conditions of practical interest the approximations associated with the use of the one-dimensional flow theory are shown to be small.Flow with a developing velocity profile and flow in a bend are then analysed. Introducing approximations revealed in the analysis of fully-developed flow, a simple relation is obtained between the variation of mean flow properties along the duct under incompressible and compressible flow conditions. This relation may be written in the same form as the corresponding relation derived using the one-dimensional flow theory. In a similar manner to one-dimensional flow theory, the relation is readily extended to apply over a series of components of constant cross-sectional area.The results of the analysis are also presented in terms of static and total pressure loss coefficients. This form of presentation demonstrates that there are appreciable effects of Mach number, on the pressure loss coefficients, where they are often assumed to be small.The analysis does not enable the variation of the mean flow properties to be calculated ab initio. Its application is to be found in problems where a knowledge of the performance of a component, or series of components, is required under compressible flow conditions, the performance under incompressible flow conditions already being available from theoretical or experimental data.A comparison of predicted and experimental data for flow in bends and flow in combinations of duct components shows good agreement over much of the subsonic speed regime.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

scholarly journals Forensic Investigation of Four Monitored Green Infrastructure Inlets

Water ◽  
2021 ◽  
Vol 13 (13) ◽  
pp. 1787
Author(s):  
Leena J. Shevade ◽  
Franco A. Montalto
Keyword(s):  
Measurement Uncertainty ◽  
Green Infrastructure ◽  
Stormwater Management ◽  
Catchment Area ◽  
Low Flow ◽  
Inflow Rate ◽  
Forensic Investigation ◽  
Flow Conditions ◽  
The Mean

Green infrastructure (GI) is viewed as a sustainable approach to stormwater management that is being rapidly implemented, outpacing the ability of researchers to compare the effectiveness of alternate design configurations. This paper investigated inflow data collected at four GI inlets. The performance of these four GI inlets, all of which were engineered with the same inlet lengths and shapes, was evaluated through field monitoring. A forensic interpretation of the observed inlet performance was conducted using conclusions regarding the role of inlet clogging and inflow rate as described in the previously published work. The mean inlet efficiency (meanPE), which represents the percentage of tributary area runoff that enters the inlet was 65% for the Nashville inlet, while at Happyland the NW inlet averaged 30%, the SW inlet 25%, and the SE inlet 10%, considering all recorded events during the monitoring periods. The analysis suggests that inlet clogging was the main reason for lower inlet efficiency at the SW and NW inlets, while for the SE inlet, performance was compromised by a reverse cross slope of the street. Spatial variability of rainfall, measurement uncertainty, uncertain tributary catchment area, and inlet depression characteristics are also correlated with inlet PE. The research suggests that placement of monitoring sensors should consider low flow conditions and a strategy to measure them. Additional research on the role of various maintenance protocols in inlet hydraulics is recommended.

scholarly journals Quantifying the Effects of Wave—Current Interactions on Tidal Energy Resource at Sites in the English Channel Using Coupled Numerical Simulations

Energies ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 3625
Author(s):  
Jon Hardwick ◽  
Ed B. L. Mackay ◽  
Ian G. C. Ashton ◽  
Helen C. M. Smith ◽  
Philipp R. Thies
Keyword(s):  
Wave Model ◽  
Tidal Energy ◽  
English Channel ◽  
Flow Conditions ◽  
Mean Flow ◽  
Radiation Stress ◽  
Large Wave ◽  
Stress Gradients ◽  
The Mean ◽  
Flow Power

Numerical modeling of currents and waves is used throughout the marine energy industry for resource assessment. This study compared the output of numerical flow simulations run both as a standalone model and as a two-way coupled wave–current simulation. A regional coupled flow-wave model was established covering the English Channel using the Delft D-Flow 2D model coupled with a SWAN spectral wave model. Outputs were analyzed at three tidal energy sites: Alderney Race, Big Roussel (Guernsey), and PTEC (Isle of Wight). The difference in the power in the tidal flow between coupled and standalone model runs was strongly correlated to the relative direction of the waves and currents. The net difference between the coupled and standalone runs was less than 2.5%. However, when wave and current directions were aligned, the mean flow power was increased by up to 7%, whereas, when the directions were opposed, the mean flow power was reduced by as much as 9.6%. The D-Flow Flexible Mesh model incorporates the effects of waves into the flow calculations in three areas: Stokes drift, forcing by radiation stress gradients, and enhancement of the bed shear stress. Each of these mechanisms is discussed. Forcing from radiation stress gradients is shown to be the dominant mechanism affecting the flow conditions at the sites considered, primarily caused by dissipation of wave energy due to white-capping. Wave action is an important consideration at tidal energy sites. Although the net impact on the flow power was found to be small for the present sites, the effect is site specific and may be significant at sites with large wave exposure or strong asymmetry in the flow conditions and should thus be considered for detailed resource and engineering assessments.

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