Enhancement to the Traditional Ellipse Law for More Accurate Modeling of a Turbine With a Finite Number of Stages

2017 ◽  
Vol 139 (11) ◽  
Author(s):  
W. F. Fuls
Keyword(s):  
Finite Number ◽  
Critical Pressure ◽  
Pressure Ratio ◽  
Axial Flow ◽  
Nozzle Flow ◽  
Flow Equations ◽  
Numerical Studies ◽  
Multistage Turbine ◽  
Definition Of ◽  
Stage Analysis

This paper studies the origin and applicability of the traditional Stodola ellipse law and demonstrates its deficiencies when applied in certain conditions. It extends the equation by Cooke and Traupel through the definition of a semi-ellipse law. This new law produces more accurate results as compared to the ellipse law (EL), especially for turbines with a low number of stages. It does, however, require knowledge of the choking behavior of the turbine, as well as an appropriate pressure ratio exponent. Through numerical studies and careful application of nozzle flow equations, correlations were developed to predict the critical pressure ratio of a multistage turbine, taking nozzle and blade efficiency into account. Correlations are also presented to obtain an appropriate pressure ratio exponent to use in the semi-ellipse law. A methodology is proposed through which the necessary semi-ellipse law terms can be calculated using only design base conditions and estimates of efficiencies. This was successfully validated on a steam turbine. The semi-ellipse law is believed to be the most accurate way of modeling an axial-flow multistage steam or gas turbine from design base conditions, without requiring a stage-by-stage analysis.

Origins of Loss Within a Multistage Turbine Environment Under Conditions of Partial Admission

1997 ◽  
Author(s):  
Guy R. Wakeley ◽  
Ian Potts
Keyword(s):  
Pressure Ratio ◽  
Axial Flow ◽  
Navier Stokes ◽  
Multi Stage ◽  
Air Turbine ◽  
Partial Admission ◽  
Multistage Turbine ◽  
Bending Stresses ◽  
Swallowing Capacity ◽  
Turbine Design

A partially admitted first stage is routinely used in a wide variety of turbo-machines to match the turbine swallowing capacity to the cycle pressure ratio over a range of outputs. Such a configuration is often favoured for applications in which optimised part-load efficiency is a design requirement. Partial admission is achieved by dividing the stator row into discrete arcs, each of which can be separately supplied with fluid. This arrangement creates circumferential discontinuities and considerable unsteadiness in the flow field within the intra-stage gap, and this unsteadiness can propagate through several downstream rows of fully admitted blading. In the current work an unsteady, multi-stage, multi-passage, Navier-Stokes solver has been validated against experimental results from a multistage axial flow air turbine. Interstage traverses of static and total pressure are shown to agree well with the CFD predictions, and the measured and predicted partial admission loss is compared with published correlations. It is further shown that the operating point of downstream stages is influenced by the degree of partial admission in the first stage. Additionally, increased alternating blade bending stresses are predicted. These phenomena are not included in any published turbine design methods, and are discussed within the context of large output steam turbine optimisation.

A Note on the Critical Pressure Ratio Across a Fluid Meter

1973 ◽  
Vol 95 (3) ◽  
pp. 337-341
Author(s):  
R. P. Benedict ◽  
R. D. Schulte
Keyword(s):  
Critical Pressure ◽  
Static Pressure ◽  
Pressure Ratio ◽  
Numerical Studies

The concept of critical static pressure ratio across a fluid meter is first discussed. Various formulations for critical pressure ratios are then developed and solutions are tabulated for convenience. Conclusions, based on graphical and numerical studies, are drawn as to which critical pressure ratios apply in the various supercritical formulations.

scholarly journals Axial Flow Compressor Stability Enhancement: Circumferential T-Shape Grooves Performance Investigation

Aerospace ◽  
2021 ◽  
Vol 8 (1) ◽  
pp. 12
Author(s):  
Marco Porro ◽  
Richard Jefferson-Loveday ◽  
Ernesto Benini
Keyword(s):  
Vortex Breakdown ◽  
Pressure Ratio ◽  
Axial Flow ◽  
Suction Side ◽  
Treatment Technique ◽  
Tip Leakage Flow ◽  
Stall Inception ◽  
Stall Margin ◽  
Casing Treatment ◽  
Stall Margin Improvement

This work focuses its attention on possibilities to enhance the stability of an axial compressor using a casing treatment technique. Circumferential grooves machined into the case are considered and their performances evaluated using three-dimensional steady state computational simulations. The effects of rectangular and new T-shape grooves on NASA Rotor 37 performances are investigated, resolving in detail the flow field near the blade tip in order to understand the stall inception delay mechanism produced by the casing treatment. First, a validation of the computational model was carried out analysing a smooth wall case without grooves. The comparisons of the total pressure ratio, total temperature ratio and adiabatic efficiency profiles with experimental data highlighted the accuracy and validity of the model. Then, the results for a rectangular groove chosen as the baseline case demonstrated that the groove interacts with the tip leakage flow, weakening the vortex breakdown and reducing the separation at the blade suction side. These effects delay stall inception, improving compressor stability. New T-shape grooves were designed keeping the volume as a constant parameter and their performances were evaluated in terms of stall margin improvement and efficiency variation. All the configurations showed a common efficiency loss near the peak condition and some of them revealed a stall margin improvement with respect to the baseline. Due to their reduced depth, these new configurations are interesting because they enable the use of a thinner light-weight compressor case as is desirable in aerospace applications.

scholarly journals A new method for calculating the sonic conductance of airflow through a short-tube orifice

2017 ◽  
Vol 9 (2) ◽  
pp. 168781401668726 ◽  
Author(s):  
Fan Yang ◽  
Gangyan Li ◽  
Dawei Hu ◽  
Toshiharu Kagawa
Keyword(s):  
Flow Rate ◽  
Critical Pressure ◽  
Pressure Ratio ◽  
Momentum Equation ◽  
Diameter Ratio ◽  
Test Method ◽  
Theoretical Formula ◽  
Engineering Applications ◽  
Short Tube ◽  
Length To Diameter Ratio

In this study, we proposed a method for calculating the sonic conductance of a short-tube orifice. First, we derived a formula for calculating the sonic conductance based on a continuity equation, a momentum equation and the definition of flow-rate characteristics. The flow-rate characteristics of different orifices were then measured using the upstream constant-pressure test method in ISO 6358. Based on these test data, the theoretical formula was simplified using the least squares fitting method, the accuracy of which was verified experimentally. Finally, the effects of the diameter ratio, the length-to-diameter ratio and the critical pressure ratio were analysed with reference to engineering applications, and a simplified formula was derived. We conclude that the influence of the diameter ratio is greater than that of the length-to-diameter ratio. When the length-to-diameter ratio is <5, its effect can be neglected. The critical pressure ratio has little effect on the sonic conductance of a short-tube orifice, and it can be set to 0.5 when calculating the sonic conductance in engineering applications. The formula proposed in this study is highly accurate with a mean error of <3%.

Numerical Studies of Novel Aero Engine Secondary Combustors for Low-NOx Emissions

2020 ◽  
Author(s):  
Andrew Rolt ◽  
Victor Martínez Bueno ◽  
Mirko Romanelli ◽  
Xiaoxiao Sun ◽  
Pierre Gauthier ◽  
...  
Keyword(s):  
Thermal Efficiency ◽  
Pressure Ratio ◽  
Flow Region ◽  
Nox Emissions ◽  
Low Oxygen ◽  
Engine Operation ◽  
Horizon 2020 ◽  
Novel Technologies ◽  
Numerical Studies ◽  
Aero Engine

Abstract Gas turbine thermal efficiency and fuel burn are very dependent on turbine entry temperature and overall pressure ratio (OPR). Unfortunately, increases in these two parameters compromise other key aspects of engine operation and tend to increase emissions of nitrogen oxides (NOx). The European Horizon 2020 ULTIMATE project researched advanced-cycle aero engines with synergistic combinations of novel technologies to increase thermal efficiency without increasing emissions. One candidate technology was the addition of secondary combustion to increase the mean temperature of heat addition to improve thermal efficiency while limiting the primary combustor flame temperatures and NOx formation. However, an overall reduction in NOx also requires the secondary combustor to be a low-NOx design. This paper describes numerical studies carried out on novel aero engine secondary combustor concepts developed in two MSc-thesis research projects. The studies have explored the potential of oxy-poor-flame combustion concepts. These annular combustor designs featured two distinct regions: (i) the vortex zone, which promotes recirculation of combustion products, a prerequisite for low-oxygen combustion, and (ii) a through-flow region where part of the incoming flow bypasses the vortex before the flows mix again. These studies have demonstrated the advantages and some limitations of the proposed designs and emissions assessments in comparison with previous secondary combustor studies. They suggest very low NOx is achievable with oxy-poor combustion, but will be more difficult if the incoming oxygen levels are above 10%. More-accurate assessments will require LES modelling and inclusion of the primary combustor in the simulations. However, if the low overall NOx emissions would include relatively higher levels of nitrous oxide (N2O) then this might raise concerns with respect to global warming.

Numerical Efforts of Aerodynamic Re-Design in a Single-Stage Transonic Axial Compressor: Part 1 — Stator Design

2017 ◽  
Author(s):  
Justin (Jongsik) Oh
Keyword(s):  
Pressure Ratio ◽  
Axial Compressor ◽  
Axial Flow ◽  
Single Stage ◽  
Design Flow ◽  
Design Parameters ◽  
Original Design ◽  
Circular Arc ◽  
Surge Margin ◽  
Flow Compressor

In many aerodynamic design parameters for the axial-flow compressor, three variables of tailored blading, blade lean and sweep were considered in the re-design efforts of a transonic single stage which had been designed in 1960’s NASA public domains. As Part 1, the re-design was limited to the stator vane only. For the original MCA (Multiple Circular Arc) blading, which had been applied at all radii, the CDA (Controlled Diffusion Airfoil) blading was introduced at midspan as the first variant, and the endwalls of hub and casing (or tip) were replaced with the DCA (Double Circular Arc) blading for the second variant. Aerodynamic performance was predicted through a series of CFD analysis at design speed, and the best aerodynamic improvement, in terms of pressure ratio/efficiency and operability, was found in the first variant of tailored blading. It was selected as a baseline for the next design efforts with blade lean, sweep and both combined. Among 12 variants, a case of positively and mildly leaned blades was found the most attractive one, relative to the original design, providing benefits of an 1.0% increase of pressure ratio at design flow, an 1.7% increase of efficiency at design flow, a 10.5% increase of the surge margin and a 32.3% increase of the choke margin.

On the Dynamic Isotropy of Mechanisms With Two Degrees of Freedom

2005 ◽  
Author(s):  
Raffaele Di Gregorio ◽  
Alessandro Cammarata ◽  
Rosario Sinatra
Keyword(s):  
Finite Number ◽  
Degrees Of Freedom ◽  
Point Of View ◽  
Closed Curves ◽  
Special Cases ◽  
Dynamic Performances ◽  
Definition Of ◽  
Geometric Locus

The comparison of mechanisms with different topology or with different geometry, but with the same topology, is a necessary operation during the design of a machine sized for a given task. Therefore, tools that evaluate the dynamic performances of a mechanism are welcomed. This paper deals with the dynamic isotropy of 2-dof mechanisms starting from the definition introduced in a previous paper. In particular, starting from the condition that identifies the dynamically isotropic configurations, it shows that, provided some special cases are not considered, 2-dof mechanisms have at most a finite number of isotropic configurations. Moreover, it shows that, provided the dynamically isotropic configurations are excluded, the geometric locus of the configuration space that collects the points associated to configurations with the same dynamic isotropy is constituted by closed curves. This results will allow the classification of 2-dof mechanisms from the dynamic-isotropy point of view, and the definition of some methodologies for the characterization of the dynamic isotropy of these mechanisms. Finally, examples of applications of the obtained results will be given.

Design and Development of a 12:1 Pressure Ratio Compressor for the Ruston 6-MW Gas Turbine

1982 ◽  
Author(s):  
F. Carchedi ◽  
G. R. Wood
Keyword(s):  
Gas Turbine ◽  
Test Data ◽  
Pressure Ratio ◽  
Axial Flow ◽  
Aerodynamic Design ◽  
Design And Development ◽  
Surge Line ◽  
Flow Compressor ◽  
Industrial Gas Turbine ◽  
Spanwise Flow

This paper describes the design and development of a 15-stage axial flow compressor for a −6MW industrial gas turbine. Detailed aspects of the aerodynamic design are presented together with rig test data for the complete characteristic including stage data. Predictions of spanwise flow distributions are compared with measured values for the front stages of the compressor. Variable stagger stator blading is used to control the position of the low speed surge line and the effects of the stagger changes are discussed.

scholarly journals Computational Analysis of the Pulmonary Arteries in Congenital Heart Disease: A Review of the Methods and Results

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
M. Conijn ◽  
G. J. Krings
Keyword(s):  
Congenital Heart Disease ◽  
Heart Disease ◽  
Boundary Conditions ◽  
Congenital Heart ◽  
Treatment Options ◽  
Pulmonary Arteries ◽  
Original Research ◽  
Numerical Studies ◽  
Computational Fluid Dynamics Cfd ◽  
Definition Of

With the help of computational fluid dynamics (CFD), hemodynamics of the pulmonary arteries (PA’s) can be studied in detail and varying physiological circumstances and treatment options can be simulated. This offers the opportunity to improve the diagnostics and treatment of PA stenosis in biventricular congenital heart disease (CHD). The aim of this review was to evaluate the methods of computational studies for PA’s in biventricular CHD and the level of validation of the numerical outcomes. A total of 34 original research papers were selected. The literature showed a great variety in the used methods for (re) construction of the geometry as well as definition of the boundary conditions and numerical setup. There were 10 different methods identified to define inlet boundary conditions and 17 for outlet boundary conditions. A total of nine papers verified their CFD outcomes by comparing results to clinical data or by an experimental mock loop. The diversity in used methods and the low level of validation of the outcomes result in uncertainties regarding the reliability of numerical studies. This limits the current clinical utility of CFD for the study of PA flow in CHD. Standardization and validation of the methods are therefore recommended.

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