scholarly journals A Rapid Approximate Method of Determining Axial-Flow Turbine Disk and Blade Temperatures

1967 ◽  
Author(s):  
F. M. Simpson
Keyword(s):  
Numerical Solution ◽  
Approximate Method ◽  
Temperature Profile ◽  
Computer Programming ◽  
Journal Bearing ◽  
Axial Flow ◽  
Turbine Disk ◽  
Multi Stage ◽  
Hand Calculation ◽  
Cooling Air

A method of determining the temperature profile of a single-stage axial-flow turbine disk with uncooled blades is presented. The blade temperature is also estimated. Information required for the solution is: the gas properties and velocity entering the rotor, the blade and disk geometry, the blade fastening geometry, and the disk-to-shaft attachment geometry. Impingement disk cooling may be used. The temperature of the shaft at a point near the journal bearing mutt be assumed, but it is shown that this assumption is not critical. A stepwise numerical solution, suitable for either hand calculation or computer programming, is employed. The method may be extended to multi-stage turbines. A typical example is given and the effect of changing the radius of injection of the disk cooling air is shown.

scholarly journals Spanwise Transport in Axial-Flow Turbines: Part 2 — Throughflow Calculations Including Spanwise Transport

1993 ◽  
Author(s):  
K. L. Lewis
Keyword(s):  
Aspect Ratio ◽  
Temperature Profile ◽  
Turbulent Diffusion ◽  
Axial Flow ◽  
Low Aspect Ratio ◽  
Loss Distributions ◽  
Diffusive Term ◽  
Two Stages ◽  
Throughflow Model

In Part 1 of this paper, a repeating stage condition was shown to occur in two low aspect ratio turbines, after typically two stages. Both turbulent diffusion and convective mechanisms were responsible for spanwise transport. In this part, two scaling expressions are determined that account for the influence of these mechanisms in effecting spanwise transport. These are incorporated into a throughflow model using a diffusive term. The inclusion of spanwise transport allows the use of more realistic loss distributions by the designer as input to the throughflow model and therefore focuses attention on areas where losses are generated. In addition, modelling of spanwise transport is shown to be crucial in predicting the attenuation of a temperature profile through a turbine.

Continuous adjoint aerodynamic optimization design for multi-stage gas turbine with cooling air

2017 ◽  
Vol 89 (3) ◽  
pp. 444-456
Author(s):  
Lei Chen ◽  
Jiang Chen
Keyword(s):  
Gas Turbine ◽  
Optimization Design ◽  
Adjoint Method ◽  
Air Injection ◽  
Aerodynamic Optimization ◽  
Content Type ◽  
Multi Stage ◽  
Surface Code ◽  
Cooling Air ◽  
Continuous Adjoint

Purpose This paper aims to conduct the optimization of the multi-stage gas turbine with the effect of the cooling air injection based on the adjoint method. Design/methodology/approach Continuous adjoint method is combined with the S2 surface code. Findings The optimization of the stagger angles, stacking lines and the passage can improve the attack angles and restrain the development of the boundary, reducing the secondary flow loss caused by the cooling air injection. Practical implications The aerodynamic performance of the gas turbine can be improved via the optimization of blade and passage based on the adjoint method. Originality/value The results of the first study on the adjoint method applied to the S2 surface through flow calculation including the cooling air effect are presented.

scholarly journals Solutions of the Force-Free Duffing-van der Pol Oscillator Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Najeeb Alam Khan ◽  
Muhammad Jamil ◽  
Syed Anwar Ali ◽  
Nadeem Alam Khan
Keyword(s):  
Approximate Solution ◽  
Numerical Solution ◽  
Approximate Method ◽  
Governing Equation ◽  
Laplace Transformation ◽  
Large Time ◽  
Van Der Pol Oscillator ◽  
Van Der Pol ◽  
Alternative Framework ◽  
Runge Kutta

A new approximate method for solving the nonlinear Duffing-van der pol oscillator equation is proposed. The proposed scheme depends only on the two components of homotopy series, the Laplace transformation and, the Padé approximants. The proposed method introduces an alternative framework designed to overcome the difficulty of capturing the behavior of the solution and give a good approximation to the solution for a large time. The Runge-Kutta algorithm was used to solve the governing equation via numerical solution. Finally, to demonstrate the validity of the proposed method, the response of the oscillator, which was obtained from approximate solution, has been shown graphically and compared with that of numerical solution.

Gas Temperature Profile Attenuation Through a Multistage Axial-Flow Turbine

2009 ◽  
Author(s):  
Boris I. Mamaev ◽  
Mikhail M. Petukhovskiy
Keyword(s):  
Temperature Profile ◽  
Attenuation Coefficient ◽  
Flow Model ◽  
Axial Flow ◽  
Gas Temperature ◽  
Empirical Coefficient ◽  
Flow Models ◽  
Flow Parameters ◽  
Through Flow ◽  
Full Scale Tests

Nowadays 2D through-flow models are widespread for designing and analysis of a turbine. Unlike 2D calculations, the measurements show that a non-uniform inlet gas temperature profile is strongly attenuated to the outlet of a turbine. This attenuation can be taken into account in through-flow models only using some corrective coefficients. The objective of this work was to find such an empirical coefficient. The results of full-scale tests of several power GTUs and aviation GTEs were employed to obtain values of the temperature profile attenuation coefficient in the through-flow model for various span locations of airfoil rows. During the tests detailed radial-circumferential distributions of the gas temperature upstream of each of rows and downstream of the turbines were measured (in absolute motion for stator and in relative motion for rotor). The values of the attenuation coefficient for airfoil rows of the three front stages were obtained by means comparison of experimental and computed results. The experience shows that the attenuation coefficient is easily incorporated into the 2D gas-dynamic codes. This incorporation allows spanwise distributions of flow parameters to be predicted and the airfoil geometry and cooling mass flow to be chosen more correctly.

Heat Transfer in a “Cover-Plate” Preswirl Rotating-Disk System

1999 ◽  
Vol 121 (2) ◽  
pp. 249-256 ◽  
Author(s):  
R. Pilbrow ◽  
H. Karabay ◽  
M. Wilson ◽  
J. M. Owen
Keyword(s):  
Heat Transfer ◽  
Rotating Disk ◽  
Reynolds Numbers ◽  
Turbine Disk ◽  
Cover Plate ◽  
Blade Cooling ◽  
Nusselt Numbers ◽  
Flow And Heat Transfer ◽  
Cooling Air ◽  
Plate System

In most gas turbines, blade-cooling air is supplied from stationary preswirl nozzles that swirl the air in the direction of rotation of the turbine disk. In the “cover-plate” system, the preswirl nozzles are located radially inward of the blade-cooling holes in the disk, and the swirling airflows radially outward in the cavity between the disk and a cover-plate attached to it. In this combined computational and experimental paper, an axisymmetric elliptic solver, incorporating the Launder–Sharma and the Morse low-Reynolds-number k–ε turbulence models, is used to compute the flow and heat transfer. The computed Nusselt numbers for the heated “turbine disk” are compared with measured values obtained from a rotating-disk rig. Comparisons are presented, for a wide range of coolant flow rates, for rotational Reynolds numbers in the range 0.5 X 106 to 1.5 X 106, and for 0.9 < βp < 3.1, where βp is the preswirl ratio (or ratio of the tangential component of velocity of the cooling air at inlet to the system to that of the disk). Agreement between the computed and measured Nusselt numbers is reasonably good, particularly at the larger Reynolds numbers. A simplified numerical simulation is also conducted to show the effect of the swirl ratio and the other flow parameters on the flow and heat transfer in the cover-plate system.

Stability of Multi-Stage Axial Flow Compressors

1964 ◽  
Vol 15 (4) ◽  
pp. 328-356 ◽  
Author(s):  
W. T. Howell
Keyword(s):  
Axial Flow ◽  
Rotational Frequency ◽  
Oscillatory Instability ◽  
Operating Point ◽  
Axial Flow Compressor ◽  
Multi Stage ◽  
Wide Range ◽  
Surge Line ◽  
Flow Compressor ◽  
The Stability

SummaryThe following theoretical investigation is concerned with the stability of the flow through a system composed of a multi-stage axial flow compressor followed by a throttle.Such an investigation was carried out by Pearson and Bowmer in 1949. In 1962 Pearson’s work on the analysis of axial flow compressor characteristics, and the accumulation of empirical data regarding factors affecting the surge line, re-awakened interest in the possibility of predicting the surge line of a multi-stage axial flow compressor-throttle system.In this paper the equations governing the stability of flow at any operating point in such a system are obtained by applying Kirchhoff’s laws to the associated electric circuit at that operating point, and the analysis is applied to a wide range of flows of the calculated characteristics of a seven-stage axial flow compressor.A study of the simplest compressor-throttle system is given, in which the equations of motion of the system are derived mechanically and electrically, and the range of validity of the equations and their stability are discussed in order to bring out the relation between the mathematics and physics of the simple system before applying these methods to multi-stage axial flow compressors.For the relatively simple electrical representation used in this paper for an axial compressor of n stages, there are shown to be 2n possible values of p, the transient rotational frequency, and these are determined over a sufficiently wide range of flows on the seven-stage compressor studied.As a result, a region of the compressor characteristic map can be marked out in which all the values of the transient rotational frequency have their real parts less than zero, corresponding to stability of operation, a region where at least one of the values of p is real and positive corresponding to non-oscillatory instability of operation, and an intermediate region where some of the values of the rotational frequency p are complex with positive real part, corresponding to oscillatory instability of operation.It is suggested that the non-oscillatory instability found here is associated with the surge and the line of inception of non-oscillatory instability with the surge line.

3D Unsteady Multi-Stage CFD Analysis of Combustor-Turbine Hot Streak Migration

2014 ◽  
Author(s):  
Khosro Mollahosseini ◽  
Fred G. Borns ◽  
Paul T. Couey ◽  
Jean-Charles Bonaccorsi ◽  
Alain Demeulenaere
Keyword(s):  
High Performance ◽  
Fluid Dynamic ◽  
Design History ◽  
Gas Temperature ◽  
Computer Clusters ◽  
Multi Stage ◽  
Nickel Base ◽  
Hot Streak ◽  
Turbine Airfoils ◽  
Cooling Air

With gas temperatures far exceeding the melting point of nickel-base alloys, advanced cooling schemes are essential to meet the desired mission life of turbine airfoils. Naturally, combustion systems produce gas-temperature non-uniformity in the exiting flowfield. Downstream turbine components must be tolerant to the maximum anticipated gas temperatures. On the other hand, excessive use of cooling air reduces engine efficiency and compromises combustor durability. Throughout gas turbine design history it has been the desire of Turbine Aerodynamicists to be able to compute combustor hot streak migration and mixing through multiple turbine airfoil stages. Typically, hot streak migration studies have been performed using (a) mixing-plane models between rotating and stationery domains or (b) unsteady simulations in which the flowpath annulus is represented by a segment containing airfoil counts that are integer multiples in each blade row or (c) Non-Linear Harmonic methods. With the development of highly-parallelized Computational Fluid Dynamic (CFD) codes driving high performance computer clusters simulation of combustor hot streak migration through multiple High Pressure (HP) turbine stages using an unsteady, 360° (full-annulus) model can be achieved. To this end, Honeywell, in collaboration with Numeca Corporation, has performed a study to evaluate the state-of the art for computation of the effect on second-stage HP turbine nozzle metal temperatures of combustor hot streaks migrated through the first-stage of a two-stage HP turbine.

A Numerical Solution for the Hydrodynamic Lubrication of Finite Porous Journal Bearings

1973 ◽  
Vol 187 (1) ◽  
pp. 71-78 ◽  
Author(s):  
B. R. Reason ◽  
D. Dyer
Keyword(s):  
Numerical Solution ◽  
Numerical Method ◽  
Journal Bearing ◽  
Hydrodynamic Lubrication ◽  
Approximate Solutions ◽  
Journal Bearings ◽  
Operating Conditions ◽  
Variable Porosity ◽  
Present Solution

We present a numerical solution for the operating conditions of a hydrodynamic porous journal bearing. The numerical method allows for the possibility of variable porosity in the bearing matrix, but the solution has been achieved on the assumption of matrix homogeneity. The relation between the various bearing parameters have been shown for a variety of bearing geometries and permeabilities enabling the operating conditions for this type of bearing to be better appreciated. A comparison of the present solution with approximate solutions used by other authors has been made, which indicates the useful working range of the approximate solutions.

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