Generation of the Equations for the Profile Losses Calculation in Blade Row of Axial Turbines in Design Analysis

2016 ◽  
Author(s):  
Oleg Baturin ◽  
Daria Kolmakova ◽  
Aleksey Gorshkov ◽  
Grigorii Popov
Keyword(s):  
Experimental Data ◽  
Statistical Analysis ◽  
Optimization Techniques ◽  
Distribution Law ◽  
Axial Turbine ◽  
Comparison Results ◽  
Profile Losses ◽  
Axial Turbines ◽  
New Equation ◽  
Profile Loss

The paper proposes a method for evaluating the reliability of models for estimating the energy losses in the blade rows of axial turbines, based on the statistical analysis of the experimental data deviation from the calculated. It was shown that these deviations are subject to the normal distribution law and can be described by mathematical expectations μΔξ and standard deviation σΔξ. The values of profile losses were calculated by five well-known models for 170 different axial turbines cascades, representing the diversity of turbines used in aircraft gas turbine engines. The findings were compared with experimental data. Comparison results were subjected to statistical analysis. It was found that the best model to describe the profile losses in axial turbines is model that has been developed in Central Institute of Aviation Motors (Russia). It allows the calculation of profile losses deviating from the actual values of losses by −8±84% with a probability of 95%. Taking into account the mentioned statistical criteria, a new equation was proposed based on the analysis of the profile losses nature and using mathematical optimization techniques. This equation makes possible to define the profile loss of axial turbine more accurate than the investigated models. It allows the calculation of profile loss values in the axial turbine that differ from the actual value by 10±61% with a probability of 95%. The proposed new equation takes into account more geometric and operational factors affecting the value of losses.

Selection of Models to Assess the Profile Losses in Blade Rows Using the Methods of Mathematical Statistics

2015 ◽  
Author(s):  
Oleg Baturin ◽  
Daria Kolmakova ◽  
Aleksey Gorshkov ◽  
Grigorii Popov
Keyword(s):  
Experimental Data ◽  
Turbine Engines ◽  
Gas Turbine Engines ◽  
Analysis Method ◽  
Distribution Law ◽  
Profile Losses ◽  
Calculation Results ◽  
Turbine Cascades ◽  
Axial Turbines ◽  
Selection Of

An investigation of five models used to assess the profile losses in axial turbine cascades appears in this article: Soderberg model, Ainley&Mathieson model, Dunhem&Came model, Kaker&Ocapu model and Central Institute of Aviation Motors (CIAM, Russia) model. Using them, the calculation results were compared with experimental data for 170 airfoil cascades of axial turbines. These cascades include a diversity of blade profiles of axial turbines used in aircraft gas turbine engines. Direct comparison of the calculated and experimental results did not make it possible to uniquely choose the best model. For this reason, the analysis method of loss models based on the statistical analysis of calculation and experimental data deviation was developed. It is shown that the deviations are subject to the normal distribution law. Based on the analysis of mathematical expectations μΔζ and standard deviation σΔζ, it was found that CIAM model gives the results closest to the experimental data. It shows the deviation from the real values of the loss 2±82% with a probability of 95%.

Development of an Experimental Correlation for Transonic Turbine Flow

1987 ◽  
Vol 109 (2) ◽  
pp. 246-250 ◽  
Author(s):  
F. Martelli ◽  
A. Boretti
Keyword(s):  
Experimental Data ◽  
Operating Conditions ◽  
Geometric Parameters ◽  
Blade Profile ◽  
Profile Losses ◽  
Experimental Correlation ◽  
Transonic Turbine ◽  
The Relationship ◽  
Profile Loss ◽  
Correlation Procedure

Optimization of transonic turbine bladings over a broad range of operating conditions calls for better understanding of the relationship between blade profile loss and cascade geometric parameters. In fact, many of the experimental correlations published to date have failed to take into due consideration transonic effects, while others have considered far too few of the numerous geometric parameters affecting profile loss in transonic flows. Through examination of the experimental data gathered by some 20 authors regarding the effects of the most significant blading geometric parameters on profile losses, a loss correlation procedure has been developed. The procedure is especially advantageous in that it allows continuous updating as new experimental data become available.

Improved Profile Loss and Deviation Correlations for Axial-Turbine Blade Rows

2005 ◽  
Author(s):  
Junqiang Zhu ◽  
Steen A. Sjolander
Keyword(s):  
Design Space ◽  
Axial Turbine ◽  
Profile Losses ◽  
Measured Profile ◽  
Aerodynamic Parameters ◽  
Lp Turbine ◽  
Turbine Airfoils ◽  
Turbine Design ◽  
Profile Loss ◽  
Highly Loaded

Empirical correlations continue to play an important role in the early stages of turbine design and in the optimizing of the gas path. The recent development of highly-loaded low-pressure (LP) turbines has extended the design space beyond the range of geometric and aerodynamic parameters on which the existing correlations for profile losses and deviation are based. With the aid of a large database of measured profile losses, including in-house results and recent cases from the open literature, the profile loss predictions of Kacker and Okapuu have been reviewed. As a result, a revised correlation is proposed that appears to capture much better the loss behavior of axial-turbine airfoils of recent design, including very highly-loaded LP turbine airfoils. The opportunity was also taken to extend the range of applicability of the correlation for trailing-edge deviation originally proposed by Islam and Sjolander in 1999.

Profile Loss Investigations With a S-CO2 Axial Turbine Aerofoil

2020 ◽  
Author(s):  
R. Senthil Kumaran ◽  
Dilipkumar B. Alone ◽  
Pramod Kumar
Keyword(s):  
Numerical Simulations ◽  
Brayton Cycle ◽  
Cfd Simulations ◽  
Fluid Medium ◽  
Real Gas ◽  
Linear Cascade ◽  
Profile Losses ◽  
Axial Turbines ◽  
Profile Loss ◽  
Flow Deflection

Abstract Axial turbines are being extensively designed for supercritical carbon-di-oxide (S-CO2) Brayton cycle power blocks. But very little information is available in the open literature on the aerodynamics of S-CO2 axial turbines, their aerofoils and loss mechanisms. The understanding of real gas behavior of S-CO2 inside a turbine is still very far from complete. Profile losses contribute to more than 50% of overall losses in a turbine. Hence, estimation of profile losses at the outset of the design process is very important. In the present study, the mean section aerofoil of the first stage of a 5 MWe Brayton cycle high temperature turbine is investigated for profile loss characteristics. The basic aerodynamic characteristics of the aerofoil in a linear cascade were initially studied using CFD simulations and cascade test experiments with air as the fluid medium. The aerofoil cascade is then subjected to numerical simulations with S-CO2 as the fluid medium. CFD simulations were carried out using a commercial RANS solver with SST k-ω turbulence model for closure. Air was modelled as ideal gas and S-CO2 was modelled as real gas with Refrigerant Gas Property tables generated over the appropriate pressure and temperature ranges using NIST Refprop database. Losses are also calculated using Craig and Cox loss model. Experiments were carried out by testing a linear cascade model comprising 12 two dimensional blades, in a high-speed cascade wind tunnel. Cascade tests were carried out over a range of exit Mach numbers and incidence angles with air as the working medium. Losses, flow deflection and blade loading were measured during the experiments. Scaling of the profile losses between air and S-CO2 fluid mediums were examined over a range of Mach numbers, Reynolds numbers and incidence angles. Detailed analysis of data generated from numerical simulations, experiments and loss model (mainly in the transonic regime) are discussed in this paper. Losses with S-CO2 was 1.5% lower than that of air while the flow deflection roughly remained the same.

scholarly journals Experimental Validation of Falling Liquid Film Models: Velocity Assumption and Velocity Field Comparison

Polymers ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1205
Author(s):  
Ruiqi Wang ◽  
Riqiang Duan ◽  
Haijun Jia
Keyword(s):  
Experimental Data ◽  
Particle Image Velocimetry ◽  
Velocity Field ◽  
Experimental Validation ◽  
Particle Image ◽  
Velocity Fields ◽  
Number Range ◽  
Comparison Results ◽  
Image Velocimetry ◽  
Experimental Particle

This publication focuses on the experimental validation of film models by comparing constructed and experimental velocity fields based on model and elementary experimental data. The film experiment covers Kapitza numbers Ka = 278.8 and Ka = 4538.6, a Reynolds number range of 1.6–52, and disturbance frequencies of 0, 2, 5, and 7 Hz. Compared to previous publications, the applied methodology has boundary identification procedures that are more refined and provide additional adaptive particle image velocimetry (PIV) method access to synthetic particle images. The experimental method was validated with a comparison with experimental particle image velocimetry and planar laser induced fluorescence (PIV/PLIF) results, Nusselt’s theoretical prediction, and experimental particle tracking velocimetry (PTV) results of flat steady cases, and a good continuity equation reproduction of transient cases proves the method’s fidelity. The velocity fields are reconstructed based on different film flow model velocity profile assumptions such as experimental film thickness, flow rates, and their derivatives, providing a validation method of film model by comparison between reconstructed velocity experimental data and experimental velocity data. The comparison results show that the first-order weighted residual model (WRM) and regularized model (RM) are very similar, although they may fail to predict the velocity field in rapidly changing zones such as the front of the main hump and the first capillary wave troughs.

scholarly journals New Equation for Predicting Pipe Friction Coefficients Using the Statistical Based Entropy Concepts

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 611
Author(s):  
Yeon-Woong Choe ◽  
Sang-Bo Sim ◽  
Yeon-Moon Choo
Keyword(s):  
Friction Coefficient ◽  
Accurate Determination ◽  
Mean Velocity ◽  
Friction Coefficients ◽  
Flow Discharge ◽  
Comparison Results ◽  
Flow Loss ◽  
Key Variables ◽  
New Equation

In general, this new equation is significant for designing and operating a pipeline to predict flow discharge. In order to predict the flow discharge, accurate determination of the flow loss due to pipe friction is very important. However, existing pipe friction coefficient equations have difficulties in obtaining key variables or those only applicable to pipes with specific conditions. Thus, this study develops a new equation for predicting pipe friction coefficients using statistically based entropy concepts, which are currently being used in various fields. The parameters in the proposed equation can be easily obtained and are easy to estimate. Existing formulas for calculating pipe friction coefficient requires the friction head loss and Reynolds number. Unlike existing formulas, the proposed equation only requires pipe specifications, entropy value and average velocity. The developed equation can predict the friction coefficient by using the well-known entropy, the mean velocity and the pipe specifications. The comparison results with the Nikuradse’s experimental data show that the R2 and RMSE values were 0.998 and 0.000366 in smooth pipe, and 0.979 to 0.994 or 0.000399 to 0.000436 in rough pipe, and the discrepancy ratio analysis results show that the accuracy of both results in smooth and rough pipes is very close to zero. The proposed equation will enable the easier estimation of flow rates.

scholarly journals Experimental analysis and ANN prediction on performances of finned oval-tube heat exchanger under different air inlet angles with limited experimental data

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 968-980
Author(s):  
Xueping Du ◽  
Zhijie Chen ◽  
Qi Meng ◽  
Yang Song
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Heat Exchanger ◽  
Correlation Equation ◽  
Tube Heat Exchanger ◽  
Flow Friction ◽  
Air Inlet ◽  
Comparison Results ◽  
Wide Range ◽  
Oval Tube

Abstract A high accuracy of experimental correlations on the heat transfer and flow friction is always expected to calculate the unknown cases according to the limited experimental data from a heat exchanger experiment. However, certain errors will occur during the data processing by the traditional methods to obtain the experimental correlations for the heat transfer and friction. A dimensionless experimental correlation equation including angles is proposed to make the correlation have a wide range of applicability. Then, the artificial neural networks (ANNs) are used to predict the heat transfer and flow friction performances of a finned oval-tube heat exchanger under four different air inlet angles with limited experimental data. The comparison results of ANN prediction with experimental correlations show that the errors from the ANN prediction are smaller than those from the classical correlations. The data of the four air inlet angles fitted separately have higher precisions than those fitted together. It is demonstrated that the ANN approach is more useful than experimental correlations to predict the heat transfer and flow resistance characteristics for unknown cases of heat exchangers. The results can provide theoretical support for the application of the ANN used in the finned oval-tube heat exchanger performance prediction.

scholarly journals Orthogonal contrasts: definitions and concepts

2004 ◽  
Vol 61 (1) ◽  
pp. 118-124 ◽  
Author(s):  
Maria Cristina Stolf Nogueira
Keyword(s):  
Experimental Data ◽  
Statistical Analysis ◽  
Interaction Effects ◽  
Degree Of Freedom ◽  
Extensive Review ◽  
Single Degree Of Freedom ◽  
Orthogonal Contrasts ◽  
Single Degree ◽  
Definite Structure

The single degree of freedom of orthogonal contrasts is a useful technique for the analysis of experimental data and helpful in obtaining estimates of main, nested and interaction effects, for mean comparisons between groups of data and in obtaining specific residuals. Furthermore, the application of orthogonal contrasts is an alternative way of doing statistical analysis on data from non-conventional experiments, whithout a definite structure. To justify its application, an extensive review is made on the definitions and concepts involving contrasts.

Experimental Validation of Forced Response Methods in a Multi-Stage Axial Turbine

2018 ◽  
Author(s):  
Thomas Hauptmann ◽  
Christopher E. Meinzer ◽  
Joerg R. Seume
Keyword(s):  
Experimental Data ◽  
Vibration Amplitude ◽  
Turbine Blades ◽  
Service Condition ◽  
Sensitivity Study ◽  
Forced Response ◽  
Tip Clearance ◽  
Computational Time ◽  
Reference Case ◽  
Axial Turbine

Depending on the in service condition of jet engines, turbine blades may have to be replaced, refurbished, or repaired in the course of an engine overhaul. Thus, significant changes of the turbine blade geometry can be introduced due to regeneration and overhaul processes. Such geometric variances can affect the aerodynamic and aeroelastic behavior of turbine blades. One goal in the development of the regeneration process is to estimate the aerodynamic excitation of turbine blades depending on these geometric variances caused during the regeneration. Therefore, this study presents an experimentally validated comparison of two methods for the prediction of forced response in a multistage axial turbine. Two unidirectional fluid structure interaction (FSI) methods, a time-linearized and a time-accurate with a subsequent linear harmonic analysis, are employed and the results validated against experimental data. The results show that the vibration amplitude of the time-linearized method is in good agreement with the experimental data and, also requires lower computational time than the time-accurate FSI. Based on this result, the time-linearized method is used to perform a sensitivity study of the tip clearance size of the last rotor blade row of the five stage axial turbine. The results show that an increasing tip clearances size causes an up to 1.35 higher vibration amplitude compared to the reference case, due to increased forcing and decreased damping work.

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